There are several distinct types of multiplayer modes in Video Games. This trope is a Sister Trope of Competitive Multiplayer, Co-Op Multiplayer and Massively Multiplayer.
Meta MultiplayerOnly 1 player is present playing in their own game at a time, but there are other players doing this as well.
LeaderboardsPlayers compete with other single players for performance in the game. Examples:
Succession Game (aka "Hotseat")Players take a turn in a single-player game, then relinquish control to another at a certain point in the game's progress. Almost any game can be played this way, even if it isn't part of the game design. Examples:
Non-Preemptive MultiplayerTwo individual games that take turns. The two game sessions are kept entirely separate. Both scores may be tracked and directly compared for competition. Examples:
Recorded/Ghost MatchesOne player's game is recorded from start to finish, and another player competes directly against the recorded game. Examples: