What Intelligence Tests Miss is a book about the difference between intelligence and rationality. The linked LW-article about the book should answer your questions about the difference between the two.

A short answer would be that intelligence describes how well you think, but not some important traits and knowledge like: Do you use your intelligence (are you a reflective person), do you have a strong need for closure, can you override your intuitions, do you know Bayes-theorem, probability theory, or logic?