1) Regulation. What you heard as "PSD2" - is essentially a directive by European Commission and EBA demanding banks to open up access to accounts data and payment initiation. Neither it defines by what means this access should be provided, nor when it should be available - each European country Central Bank can decide on its own.
2) Technical Specification. Examples are OpenBanking UK specification or The Berlin Group - would be groups of banks or local regulators trying to define common standards. Think of interface definition that describes both APIs as well as journeys/workflows.
3) Compliance. In the EU some of the banks (mostly large ones) are now required to be PSD2 compliant, which means they would need to expose their APIs through the standards described above. In the US, where there is no such requirement - the only way to access the bank account is to emulate a browser.
4) Third-Party Providers or Aggregators (Plaid, Teller, Tink, SaltEdge, Bud...) - would essentially provide access to the accounts of multiple banks via APIs. If you look at Plaid in the US - their codebase is probably 50%+ screenscraping/user emulation scripts in order to retrieve your accounts from e.g. Bank of America. For the EU fin-techs its a bit better, but still depends per country (remember Berlin Group vs UK OpenBanking?).