Optimizers, well, optimize. They work within a character concept to maximize a character's effectiveness.

Powergamers are not out to work with a character. A powergamer wants to have power, and so his first consideration in the game is not "what character would be fun?" but "what character would be the most powerful?". They're not as bad as the next category but can cause issues, mostly if mixed in with nonpowergamers, because the aims of the players are different.

Munchkins are also out to have power, but in a different way and with a different aim than the powergamer. The powergamer views D&D as a series of challenges that the DM is putting forth and wants to defeat them. The munchkin views D&D as a contest among everyone at the table to dominate gameplay. This means that they must be more powerful not only than the DM's challenges, but more powerful than the other players as well. Because of this, they're not interested in playing a game, the way the powergamer is. They're interested in playing a metagame, and in their view, everything that advances them helps that. Rules don't apply to their metagame and so they may ignore or overlook them.