Sorry, that was perhaps unclear, that 'they' referred to the banks, in the case of bank-bank.

Bank-bank requires that the bank at both ends supports sending/receiving to/from (as applicable) IBAN or similar yes. In the UK in practice that means 'mainstream' banks do and 'challenger' banks don't. (Monzo for example prefers to solve the problem by integrating Wise a bit into its own app.)

Wise avoids it by charging you (like paying for any other product/service) or having you transfer to its account in your country, and then sending the payment to the destination bank from its account in the same country as that, so it becomes two local transfers, one in each country.