A more thorough explanation:

Formal adjudication is a process used by administrative agencies to resolve disputes, which is governed by the Administrative Procedure Act (APA). This process is required when the statute that creates the agency mandates it. Formal adjudication involves a trial-like proceeding where parties present evidence and arguments, and an administrative law judge issues a decision with findings and conclusions.

Sections 554, 556, and 557 of the APA establish the procedural requirements for formal adjudication. Section 554 requires that the procedural protections in sections 556 and 557 be followed when the statute requires the adjudication to be “on the record after opportunity for agency hearing.” This provision is narrowly interpreted, and the statute must contain almost exactly that phrase.

For example, in Dominion Energy v. Johnson, the First Circuit found that a statute which required the adjudication to provide an “opportunity for a public hearing” did not require formal adjudication under § 554.

Sections 554, 556, and 557 require oral, trial-type proceedings for formal adjudications. Section 554(b) requires the agency to issue notice of the formal adjudication, and 554(c) ensures that interested parties have the opportunity to present their arguments. Sections 556 and 557 lay out the role of the administrative law judge and the manner by which such adjudications should proceed.

For example, in a formal adjudication, a party may present evidence and cross-examine witnesses, and the administrative law judge must issue a decision with findings and conclusions.