As I see it, their are two different sets of victory conditions. Those which give you extra ways to defeat a player, where the last player/team standing wins, and those that allow you to win the entire game outright.
Defeats
Capital - A Player loses if they lose their starting capital planet. You cannot change capital planets in this game mode.
Flagship - Each player starts with a special flagship unit. If the flagship is destroyed that player is defeated.
Wins
Diplomacy - They supposedly revised it but to be honest I haven't played it myself.
Research - When this mode is enabled, a very expensive tier 8 civic tech can be research after you research 50 other techs. The player who researches it first will win.
Occupation - A special occupation planet spawns with heavy militia on a special star system. If a player takes it and holds it long enough they'll win.
