Great question! This was unclear to me at first as well, so I asked one of the devs. And the answer is "yes." Transfers between users of the same mint are an identical UX (lightning invoice / payment), it is simply that the lightning settlement happens internally and instantly.

Source: https://github.com/fedimint/fedimint/blob/734f1414298816ef36ae5ca1299049556276ebd6/ln-gateway/src/lib.rs#L184-L190