Re:
I'll probably confuse them in my mind right now, but the difference IS in the grip.
Underhand Grip - works biceps more and imparts a narrower back exercise. These will kill your back and biceps, in a good way.
Overhand Grip - Much like weighted pull downs, but they're akin to climbing. Very difficult, too.
You can do a mixture as you press yourself to accomplish more of them. Normally I do Pullups (I'll refer to these as Overhand Grips) for several sets. If my progress fumbles, I'll switch to Chin Ups (I'll refer to these as Underhand Grips).
I either exercises until I fail at making progress, normally after deadlifts. If I want to push myself, I might add in Heavy Wide Back PullDowns. Anything to get more reps in for my back. At least for me, I never want to leave the gym feeling like I left with any extra in my pullups or chinups. For those just starting these, a few reps might be difficult, so rather than do 1 or 2 and just fall, I would RECO doing 1, then 1, then 1, then 1, then holding the position, or adding a little weight if you could only do 1. And perhaps do a heavy weighted Pulldown too. Anything to get progress. The strength from the pullups/chinups is not equivalent, but it is transferable. Meaning, if you're 180, and you do 5 pull downs at 180, you won't do 5 pullups, BUT, you can make progress this way. Also, as your deadlifts improve, so too will your back strength. But each week it should be a minor improvement in some way that will end up in adding 1 rep more soon...
A-Unit