What´s the difference between a game director, producer and designer?

A director has a general idea for a game, tells it to the team, and checks up on the progress every now and then to see if it fits with his idea
A producer is a money-grubbing fiend who alters the idea in any way that he believes can cause the game to make more sales
A designer takes the director's idea and tries to flesh it out and alter it so that it makes sense in a videogame setting
These definitions may or may not be complete bullshit

Producers are in charge of the business/management/deal-making aspects.

Directors & designers are in charge of the creative aspects, with the director being the higher authority (if there is one at all).

Responsibilities and involvement will vary production-by-production.

Director: ideas guy
Producers: getting money and marketing
Designer: the actual workhorse