Adding to AJSakowski's statement a 4 jaw chuck can be used to fabricate cams, and bore off center holes. I just finished 2 sets of cams for a sheet metal brake. One set was to make fine adjustments on the grip of the upper platen, the other set were the ones used to open and close the platen. Both sets required a 4 jaw independent chuck.
As for taking more time to dial in a 4 jaw, I would agree that in the beginning it will take considerably longer. However the more practice you get the less time it will take. After many years of practice I find a 4 jaw independent more often than not the go to chuck. It generally takes less than a minute to dial a 8" or 10" 4 jaw to within .001". That's close enough for most work. It can get tedious to dial into .", but then again I don't know of a 3 jaw scroll chuck that's capable of that close tolerance.
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The steps on the outside of the 3 jaw's jaws are for holding a part by it's bore, you can get a set with the jaws the other way around (Like in the thumbnail of doubleboost's video) for holding larger parts on the outside.The numbers on the jaws don't relate to which channel they go in, they tell you which order to put them in. If you take the jaws out, you can see the "Scroll" inside the chuck (Imagine a thread on the face of something), if you wind it around you'll see the start of it pass one of the slots, you need the #1 to be the first to engage with the scroll, #2 & 3 go in the next two slots.You can get 4 jaw self centering chucks, they have a bit more holding power than a 3 jaw (I assume, not sure how you could fairly compare it) and are useful for holding square stock. One limitation of them is they tend to have a smaller centre bore then the equivalent 3 jaw.Self centering chucks aren't very repeatable (If you turn a part, take it out of the chuck, then put it back in, chances are it'll have a bit of run-out), this is where the independent jaw chuck comes in; you have to dial the part in, so it's as good as you set it to be. Another solution if you want repeatability is a collet chuck, but they're expensive and require a large set of collets.You also get 6 jaw chucks (Usually only on bigger lathes), basically just a three jaw with extra holding oomph.Pointless chuck trivia; there are even 2 jaw chucks, but they tend to be exclusively for CNC/production lathes, as the jaws are not hardened and need to be machined to fit the part being produced.
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