The main difference between the chin-up and the pull-up is the grip taken on the bar, and how that grip impacts which muscles are used in the movement. The name itself refers to the height at which you pull your body up — just to chin level — but this is also a consequence of hand position.
The chin-up has you take a supinated grip on the bar (palms facing you), which increases the amount of biceps used, whereas the pull-up uses relatively more back and less biceps due to the pronated grip (palms facing away).