Final bosses are generally the ones responsible for the incident that the game is based around. Extra bosses are usually unrelated to the incident, but have connections to other characters or events in the game. So in a story sense, no, extra bosses are not "true finals," though it is quite possible to argue this for Yukari and Nue. And in a gameplay sense, they're more like the optional superbosses you unlock in a New Game Plus. You have to get the true ending before you're able to access extra bosses, and in a couple cases you have to do it multiple times.
As for Suika, I'm no music expert, but I'd say that they're different pieces arranged around the same theme. Also of note is that this theme also is reprised for part of the SWR ending as well.