Asymmetry: (Every player is different) The game requires more than one player, but each player has entirely different goals and rules.

Collaborative Casual/Hardcore: (Two players: one casual, one hardcore) Collaborative play for two, but one player has more to do than the other (or the difficulty level is different between them).

I know what you did last…: (Game changes between sessions) The game mechanics or content will change in the next play session, based on the actions taken in the previous session.