To claim a given conformance level, a site must meet every success criterion at that level and every level below it, so AA conformance requires meeting all A and AA criteria together. AAA is intentionally not recommended as a site-wide target by the W3C itself, since some AAA criteria (like requiring sign-language interpretation for all video) aren’t achievable for every type of content.
Level AA is the level referenced by essentially every accessibility law worldwide, including the ADA, Section 508, and the European Accessibility Act.