How do they differ? Is one better for certain sports applications than others?
Chin ups have the hands facing you, while pull ups have the hands facing away from you. But these are only two basic variations.
Thibaudeau has a good article on improving the pull up exercise:
http://www.t-nation.com/readTopic.do?id=459275
It should be noted that when you have the palms facing each other during the movement, it is also called a chin up, at least any time I remember having read the term.
Chinups should be a bit easier than pull-ups if you’re just starting off, at least that’s the way it is for me.
For instance, I can do fourteen chins but only ten pulls.
You’ll find pull-ups (palms facing away) will hit your lats more and chin-ups (palms facing towards you) will have more bicep involvement.
Part of the issue is grip - it’s much easier to get a tight grip with your thumb with hands fancing towards your face.
Try them all though. A good thing to do at the start is do as many pull-ups as you can, then as many chin-ups as you can, then pull-ups, then chin-ups and so on.
There are some serious chin experts on the forums here so hopefully they’ll have something to say as well.
I’m no expert, but the only sport I can see any correlation to for pulls or chins is rock climbing, and here it is pull-ups that would benefit rock climbing.
Perhaps another the reason chins work your biceps better than pulls is because of the insertion point of your biceps: it is on your radius, so when you rotate your wrists to do a pull, the bicep is less stressed because the tendon is partially wrapped around the radius.
I do both supersetted, weighted chins first because of my tendonitis, then I drop the weight and do pulls.