Grammatically, they function differently. Let's take the phrase "She went home." Might is a modal verb, which means only the base form of a verb can follow. No conjugations. "She might go home." (If she's still here and there's a weak possibility that she will go. A guess about the future.) "She might have gone home." (If she is not here and you really don't know what happened. Still a weak possibility. A guess about the past.) Possibly and probably come right before the verb. "She probably went home." "She possibly went home." (This is a little uncommon.) Maybe comes before the statement. "Maybe she went home."