A Fatboy is an adjustable. I assume you meant the difference between a Fatboy and a Slim Adjustable. The handle on the Fatboy is noticeably thicker than the handle on a Slim Adjustable. It isn't always easy to tell from online pictures.
Calling Fidgit!! Calling Fidgit!! He has a great post that details this difference with a great explanation on what to look for. I will try to find the link for you.