If Polbank (forgive me for the bastardized names) wants to give 1M USD to Bankpolska, they either need to ship cash (which can be done but is expensive or tricky) or have a specific bilateral agreement betwene them (which can be done and is done sometimes, but linking every bank with every other bank bilaterally does not scale), or need some interbank settlement system that will do that, but there's no such system in which they can participate. E.g. there's Fedwire but neither Polbank or Bankpolska can be direct members as far as I understand (they generally are not members; I'm not certain if it's caused by some strict limitation or just practicalities and costs.)

So the standard means is to use 'correspondent banks' e.g. USA banks that do that for them. Polbank might have an USD account with Chase or Citi, and Polbank can ask Chase (via a SWIFT message usually) "hey transfer $1m from our account to Bankpolska, it's cover for a customer deal #1234" - but this means that the transaction "goes through" USA.

Alternatively, multinational banks may have branches in both USA and Poland and so they can be direct participants and settle this directly, however, then it would involve a Fedwire transfer (in USA, subject to USA laws and limitations) between Polbank USA branch and Bankpolska USA branch.

That's standard practice for pretty much every currency. EUR settlement between two American banks usually (not always, there are various options) goes through EU, RUB settlement usually goes through Russia, etc.

If there's a sufficient need, Polish banks could establish an interbank settlement system through which they could transfer USD directly (e.g. similar to the one they have for transfering Polish zloty), but it's a hassle and has costs, so currently they have not done so because for them it's generally not a problem to route all USD payments through USA.