Checkmate ends the game immediately, provided the move producing it was legal (Art. 5.1.1); Resignation: a player who resigns loses immediately, unless the position is one in which the opponent cannot possibly checkmate (Art. 5.1.2); Time: a player who does not complete the prescribed moves in th...
Why people argue about this
People often assume that if a player resigns their game, it's automatically over just because they said they give up - forgetting that the other player must also acknowledge this resignation for the game to end. The confusion arises because both players need to agree on the outcome for it to be valid.