Do UN and AP count as separate victory conditions? The game records them both as Diplomatic Victory, but xotm has separated them.
Yes. For the purposes of this game, there are seven victory conditions possible:
Time, Religious, Diplomatic, Culture, Conquest, Domination, and Space Race
As stated, if all you fulfill is conquest+domination, that will only count as one. But if you fulfill any other victory, either conquest or domination is sufficient as a second VC, you don't need both.