An Amnesia game is a larp where the character starts out missing memories. This may be a true tabula rasa, where the players start out with, at most, a short description of their character's general affect -- or the characters may be incomplete (possibly even seeming complete, at first), with holes or false memories replacing the missing memories at first.
Some (including the first, Tabula Rasa) amnesia games feature fully-written character sheets that are re-accquired over the course of the game.
However, this is not the only possible mechanism. A game where workshop techniques are used to fill in missing memories over the course of the game, allowing the players to build on the starting emptiness rather than discover it would still be considered an amnesia game.
Any game where characters acquire new memories via a diegetic technique might be considered loosely an amnesia game as well -- for instance, a game where the characters acquire past life memories over the course of the game, or even memories of future or parallel lives can be considered an amnesia game even though the characters' memories are technically complete at the game's start.