Which types of bank transactions are classified as international?

Typically any transactions that involve an external ledger and settlement with another bank (be it correspondent or direct respondent bank), which is outside the country the current bank is operating in.

Most of such transactions are either incoming payments or outgoing payments. The payment may be direct fiat money or a monetary instrument that is being executed.

Even the authorization of such a transaction would be considered an international transaction as that would need to be settled in T+X, where X is some time frame from the transaction date “T”.