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?
This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.