Player Elimination, or a Strict Elimination, refers to a collection of mechanics which removes a player’s ability to participate in a game, typically in an irreversible manner on a per-match basis. While the term could be applied to two-player or one-player games, it is usually only used in the context of many-player games.
Logical Elimination is a super-type of Player Elimination, where the player in question is still able to participate in the game yet does not have any possibility of achieving a win condition.
Having a significant time-gap between a player being logically and strictly eliminated is generally a bad thing for the game in question1, as it can force players to play a hopeless situation for an extended period and leads to situations of kingmaking or griefing.
Elias, G. S., Garfield, R., & Gutschera, K. R. (n.d.). Characteristics of Games. MIT Press. ↩