I would say that all creationists believe in Intelligent Design, but not all believers in Intelligent Design are creationists.
I don't agree with that. Because ID means that everything did some evolution (at least microevolution) according to Gods great plan. Quite a few creationists (like those on AiG) believe that Microevolution without any special sort of guidance took place, for all animals evolved from those Noah took with him in his ark. And since there's no place in Genesis where it's stated that God made animals change according to that great plan of His, they probably won't even argue that point.
