For the purposes of the game, "defeating" a monster involves beating it in combat or removing it from play in such a way that you do not have to Run Away. This means that if a Wizard casts a charm spell, or a munchkin uses a Pollymorph Potion, or something else happens that ends a fight without the munchkins Running Away, the monster is defeated. This may or may not grant Treasures, depending on the method of defeat; assume it does not unless the card or method says otherwise.
"Killed" means that you defeated the monster with your Level and bonuses in combat, or used some card or special ability that specifically states that it kills the monster. For this, you get levels and Treasure.