Eclectic Company, Inc. (“Eclectic”) appeals the district court’s grant of summary judgment on behalf of Staffco Construction, Inc. (“Staffco”) in its cross-claim for quantum meruit relief under the Miller Act and for breach of contract. Because the district court concluded correctly that no triable issues of fact remained in this case and that Staffco was entitled to judgment as a matter of law, we affirm.

FACTS

On July 8, 1996, Wright-Patterson Air Force Base (“WPAFB”) in Dayton, Ohio, sought bids from contractors to renovate the basement of Building 262 at WPAFB. WPAFB generated full-size drawings of the project and requisitioned copies of the drawings from the Government Printing Office (“GPO”). The GPO outsourced the project to a local, privately-owned print shop that mistakenly produced half-size copies of the drawings. The print shop did not label the drawings as reduced in size.

After receiving the reduced drawings, WPAFB rejected them and the GPO required the print shop to reprint the drawings in the proper size. The print shop did so, and WPAFB received full-size drawings on August 7, 1996. After it received the full-size drawings, however, WPAFB failed to destroy all the remaining half-size drawings.

Staffco obtained a bid package from WPAFB, which contained accurate drawings, and sought bids from subcontractors to join its proposal. Eclectic provided the only bid for the HVAC and plumbing work, which Staffco accepted and incorporated into its proposal. Staffco did not know, however, that Eclectic had mistakenly received the half-size drawings from WPAFB and had based its proposal on the incorrect drawings. Staffco saw nothing on the face of Eclectic’s bid to indicate that the bid was based on incorrect dimensions.

On December 6, 1996, Staffco entered into a subcontract agreement with Eclectic to perform the HVAC and plumbing work, which incorporated by reference the terms of the bid solicitation and Staffco’s anticipated contract with the Government. On December 12, the Government awarded the contract to Staffco.

On April 1, 1997, WFAFB issued Staffco a notice to proceed with the project. After the notice was issued, Eclectic reviewed the full-size drawings and first became aware that its bid was predicated on half-size drawings. Eclectic’s president, Ronald Wantz, and project manager, Steve Eick, met with Staffco’s president, Mike Stafford, to discuss the problem. Wantz indicated to Stafford that Eclectic could not proceed with the project because it had bid on half-size drawings. Stafford replied that “Staffco had a contract with Eclectic which it expected Eclectic to perform, but that ‘the [Government had a procedure that we would go through to resolve these problems and that [Eclectic] would be paid one way or another.’” Wantz admitted that he understood this assurance to mean that Staffco intended to ask the Government to change its contract in light of the shortfall and then adjust the subcontract agreement with Eclectic. Eclectic performed and claimed an additional $417,075.23 to complete the project.

*455First, Staffco petitioned the Air Force directly for an adjustment of the contract fee. The contracting officer who reviewed Staffco’s petition rejected the claim, determining that the correct dimensions were easily ascertainable from the half-size drawings, that Eclectic failed to participate in a site visit, and that Eclectic failed to provide any evidence of a mistake in its bid. Proceeding in Staffco’s name, Eclectic appealed this decision to the Armed Services Board of Contract Appeals (“ASBCA”).

The ASBCA also rejected Eclectic’s claim for additional compensation. Although the ASBCA concluded that the Government was responsible for Eclectic receiving the half-size drawings, the ASBCA first noted that the bid package encouraged potential bidders to make a physical site visit and inspect the work site. Second, the ASBCA noted that Eclectic had bid on projects at WPAFB in the past and was aware that the drawings it received were not the same size as drawings it had received from the base in the past. Despite the fact that Wantz contacted WPAFB to see if other drawings were available, the ASBCA found that Eclectic failed to notify WPAFB that the drawings may have been inaccurate. Third, with regard to the drawings themselves, the ASBCA found that:

The half-size drawings at issue contained the statement “SCALE 1"=20'.” Immediately above that written scale was a graphic bar scale in which one measured inch was denoted as “40'.” According to professional engineer C. Jeffrey Tefend, who designed the project and prepared the mechanical drawings, the graphic scale is the “true” scale of a drawing. As Mr. Stafford, Mr. Tefend and Mr. Balsamo agreed, the graphic scale remains accurate despite a reduction in drawing size. Whereas the written scale was incorrect on the half-size drawings, the graphic scale was correct. A comparison of the written scale and the graphic scale would have revealed that the drawings were half-size.

J.A. at 183-84 (emphasis added). Moreover, the ASBCA noted, the drawings Eclectic received contained “hard dimensions” — numbers printed on the drawing to indicate dimensions, saving the reader from scaling them off — that conflicted with the written scale. Because of the conflict of the written scale with the graphic scale and the hard dimensions, the ASBCA concluded that the drawings Eclectic received were patently ambiguous.

Having concluded that the drawings were patently ambiguous, the ASBCA followed the Federal Circuit’s rule that, when there is an ambiguity on the face of the drawings in a government solicitation, the ambiguity is construed against the potential bidder unless the bidder inquires as to the meaning of the ambiguity. See Triax Pacific, Inc. v. West, 130 F.3d 1469, 1474-75 (Fed.Cir. 1997). The ASBCA concluded that the ambiguities in the drawings were obvious, but Eclectic nonetheless proceeded in the face of those ambiguities rather than discharge its duty to inquire.

After the ASBCA proceeding, Spectrum Controls (“Spectrum”), a subcontractor of Eclectic and not a party to this appeal, initiated in the district court this proceeding, against Staffco and Eclectic, for compensation pursuant to its installation of temperature controls in the project. Eclectic then filed a cross-claim against Staffco, alleging: (1) a claim for compensation against Staffco’s payment bond under the Miller Act, 40 U.S.C. § 270b(a), (2) breach of contract, (3) unjust enrichment, and (4) intentional interference with contractual relations. The district court entered summary judgment on Staffco’s be*456half with regard to each of these claims. Eclectic appeals that determination with regard to the Miller Act claim and the contract claim.

The district court concluded that Eclectic’s Miller Act claim was precluded by res judicata. Although Eclectic argued that it was not a party to the ASBCA proceeding, the district court rejected this contention, concluding that Eclectic “had complete control” of those proceedings, and even if it had not, Eclectic was in privity of contract with Staffco. Eclectic also argued that the issues presented in its cross-claim were different from those presented before the ASBCA, but the district court rejected that contention, reasoning that the relief sought by Eclectic before the ASBCA was “precisely what Eclectic now seeks in its Miller Act claim.” Ultimately, the district court reasoned that Eclectic’s entitlement to equitable relief from its subcontract was “fully and fairly litigated in a proceeding in which Eclectic controlled the presentation in favor of equitable relief.” Therefore, according to the district court, Eclectic was barred from pursuing its Miller Act claim against Staffco.

The district court also rejected Eclectic’s claim for quantum meruit recovery under the Miller Act because Eclectic was unable to demonstrate that “the subcontract ha[d] been substantially breached or [Eclectic] ha[d] performed additional work outside the contract.” Because the ASBCA’s decision barred Eclectic from rescinding its subcontract agreement with Staffco, the district court reasoned that Eclectic could not establish the elements of its quantum meruit claim.

Regarding Eclectic’s breach of contract claim, the district court rejected Eclectic’s contention that Stafford’s statement that Eclectic would be paid “one way or the other” created an oral modification to the subcontract that Staffco subsequently breached. The district court reasoned that, even assuming Stafford had made the promise, the promise was unsupported by consideration and therefore unenforceable.

DISCUSSION

1. Res Judicata

On appeal, Eclectic argues against the district court’s conclusion that its Miller Act claims are barred by res judicata, contending that the issues presented in the district court litigation were different from those presented before the ASBCA. Because the ASBCA resolved the only issue in dispute, the district court correctly reasoned that the preclusive effect of the ASBCA’s earlier determination entitled Staffco to summary judgment on Eclectic’s Miller Act claim.1

The district court’s opinion in this case illustrates some of the confusion that surrounds the terms used to describe the law of prior judgments. Res judicata is a term with two different meanings. In a broad sense, the term “refers to the distinctive effects of a judgment separately characterized as ‘claim preclusion’ and ‘issue preclusion.’ ” 18 C. Wright, A. Miller & E. Cooper, Fed. Prac. & Proc. Juris.2d § 4402 (2004). In a narrower sense, res judicata is synonymous with claim preclusion. See Migra v. Warren City School Dist. Bd. of Educ., 465 U.S. 75, 77 n. 1, 104 S.Ct. 892, 79 L.Ed.2d 56 (1984) (explaining prior Supreme Court practice of using “res judicata” in a sense that “excludefs] issue preclusion or collateral estoppel”). This *457double meaning leads to confusion when a court, as in this case, deems a prior ruling to be “res judicata. ”

Although it does not use the term, Eclectic argues that its claims against Staffco are not barred by claim preclusion. Under the doctrine of claim preclusion, a final judgment on the merits by a court of competent jurisdiction bars any subsequent litigation on the same claim between the same parties, or non-parties in privity, with respect to every ground for recovery asserted in the first proceeding, as well as every ground for recovery which the parties could have raised but did not. Black v. Ryder/P.I.E. Nationwide, Inc., 15 F.3d 573, 582 (6th Cir. 1994). Non-parties may also be bound by a prior judgment if a party to the prior proceeding adequately represented the interests of the non-party. See Hansberry v. Lee, 311 U.S. 32, 43, 61 S.Ct. 115, 85 L.Ed. 22 (1940). In any event, claim preclusion does not apply unless the claim was fully and fairly litigated in the earlier proceeding.

In this case, claim preclusion does not apply. There is no indication that the ASBCA had jurisdiction to decide Eclectic’s Miller Act claim against Staffco. Because it is an appellate board, the ASBCA has no jurisdiction except to review the decision of the contracting officer. Moreover, the ASBCA’s enabling statute grants it a very limited jurisdiction to review a contracting officer’s determination “relative to a contract made by its agency.” 41 U.S.C. § 607(d) (2004). Therefore, because Staffco’s Miller Act liability to Eclectic depends on the subcontract agreement made between Staffco and Eclectic, the ASBCA lacks subject matter jurisdiction. Ultimately, because the ASBCA lacked jurisdiction to adjudicate Eclectic’s claim against Staffco, that claim could not have been fully and fairly litigated in the ASBCA proceeding.

Although claim preclusion was inapplicable, the ASBCA’s determination of a particular issue had a preclusive effect on Eclectic’s Miller Act claim. Issue preclusion “dictates that once an issue is actually and necessarily determined by a court of competent jurisdiction, that determination is conclusive in subsequent suits based on a different cause of action involving any party to the prior litigation.” Black, 15 F.3d at 582.

Issue preclusion prevents a party from relitigating a factual or legal issue decided by a court of competent jurisdiction in a prior proceeding if: (1) the issue is identical to the issue resolved in the earlier matter, (2) the issue was actually litigated and decided, (3) the resolution of the issue was necessary and essential to a judgment on the merits in the prior litigation, (4) the party to be precluded was a party, or in privity with a party to the prior litigation, and (5) the party to be precluded had a full and fair opportunity to litigate the issue. See Verizon North, Inc. v. Strand, 367 F.3d 577, 583 (6th Cir. 2004).

In this case, the ASBCA determined conclusively that Eclectic had a duty to inquire and failed to discharge that duty, and the doctrine of issue preclusion bars Eclectic from relitigating that issue. In order to establish successfully a claim under the Miller Act, Eclectic must show that: (1) it supplied materials for work in connection with the subcontract agreement, (2) it was unpaid, (3) it had a good faith belief that the materials were necessary for the specified work, and (4) its claim satisfies the jurisdictional prerequisites. United States for the Use and Benefit of Krupp Steel Products, Inc. v. Aetna Ins. Co., 831 F.2d 978, 980 (11th Cir. 1987). The ASBCA’s determination that Eclectic’s failure to inquire vitiated its entitlement to additional compensation was conclusive as to whether or not Eclectic was *458“unpaid” within the meaning of the Miller Act.

Eclectic’s contentions that it was unable fully and fairly to litigate this issue before the ASBCA are unavailing. The district court determined that Eclectic controlled the ASBCA proceeding and Eclectic has not shown this determination to be clearly erroneous. Even if the district court’s finding were in error, Eclectic was still in privity with Staffco. The ASBCA conducted a hearing, reviewed the evidence, and issued a lengthy opinion concluding that Eclectic was not entitled to additional compensation. Eclectic was, at least, in privity with a party to the earlier proceeding, and had an opportunity fully and fairly to litigate the matter. Issue preclusion thus bars Eclectic’s Miller Act claim.

2. Breach of Contract

Eclectic’s contract claim must also fail because, at minimum, the ASBCA’s determination has the collateral effect of destroying a mistake of fact defense to contract. Eclectic claims that Staffco’s promise that Eclectic would be paid “one way or the other” modified their subcontract agreement and obligated Staffco to ensure that Eclectic was paid in full for completing the contract. The district court concluded that this agreement was not supported by consideration, but Eclectic argues that its forbearance on its “right to rescind” supported the modification. Because Eclectic had no mistake of fact defense on which it could predicate a right to rescind, its asserted consideration was a nullity and there was no effective modification of the contract.

To be effective under Ohio law, a modification of a contract must satisfy the basic elements of contract formation — offer, acceptance and consideration — and must be supported by “new and distinct” consideration. Thurston v. Ludwig, 6 Ohio St. 1, 6 (1856). A party cannot offer as consideration a promise simply to do something it is already bound to do by law or contract.2 Rhoades v. Rhoades, 40 Ohio App.2d 559, 321 N.E.2d 242, 245 (1974). Therefore, Eclectic could not have offered new consideration by agreeing to fulfill its obligations under the original agreement unless it was not bound to perform in the first place.

Eclectic contends that it was not so bound, because the original agreement was predicated on a unilateral mistake of fact that rendered the original agreement voidable.3 Under Ohio law, a party claiming a unilateral mistake of contract may obtain rescission of the agreement if the mistake pertained to a material aspect of the contract, enforcement of the agreement would be unconscionable, and the mistaken party exercised ordinary diligence in entering the agreement. See Indep. Directory Corp. v. Vandenbrock, 94 N.E.2d 228, 230 (1950). Even assuming that the availability of rescission as an equitable remedy is the equivalent of not being bound to perform, the ASBCA’s conclusion that Eclectic was negligent in bidding on the project forecloses Eclectic from arguing that it exercised ordinary diligence in entering the agreement. Eclectic had a number of opportunities to discover the mistake through the exercise of diligence. Eclectic failed to conduct a site visit, to submit a written request for clarification of measurements, to verify the dimensions prior *459to bidding, and to inquire about the conflict between the written and graphic scales on the drawings.

Eclectic’s contract claim must fail because of Eclectic’s failure to inquire as to the ambiguity on the face of the drawings. Because there is also no triable issue of material fact as to Eclectic’s Miller Act claim, we AFFIRM.