Call of Duty: Black Ops III supports two-player split-screen online play in Multiplayer or Zombies game modes. Xbox One and PlayStation 4 support split-screen for up to four players in Multiplayer, but only in local play.
Split Screen is Local multiplayer for up to four players on the same system. There you can rank up just like online multiplayer, but you can choose any map, any game mode, and any rules.