They both sound to me like the same thing what's the main difference between the 2 , Like something that one can make but the other can't ?
$\begingroup$ I don't know, but the title suggests that one can hold irregularly shaped objects and hold them off-centre on a lathe. The other sounds like a regular chuck which closes and grips each jaw simultaneously so that circular or polygons with a number of sides an integer multiple of the number of jaws can be gripped concentrically with the lathe axis of rotation. $\endgroup$– TransistorJun 2, 2022 at 22:07
$\begingroup$ woodworking.stackexchange.com/questions/287/… $\endgroup$– Tiger GuyJun 2, 2022 at 22:14
$\begingroup$ I've never heard of a faceplate chuck, but a four jaw chuck has four jaws fixed onto it which are driven by worm screws and you position and tighten each jaw independently. What does faceplate chuck do? Is it just a plate with holes and grooves that you directly bolt your workpiece to? I would just call that a faceplate, not a chuck. In a mill, that would be the same difference between a vise and bolting something directly to the table. $\endgroup$– DKNguyenJun 2, 2022 at 22:32
If you mean something like this for 'faceplate chuck', then it can be viewed as a four-jaw chuck with a lower profile, designed to hold discs rather than round or square bars. There are also some similar woodworking chucks, again for discs, bowls rather than bars. They behave like a faceplate but have built-in jaws to hold the work. As they are not designed to have the work pass through them, the hole in the middle is smaller.
A faceplate can stabilise discs or irregular work, especially against cutting pressure pushing into the chuck, whereas that force will usually be resisted by friction between the jaws and the work in a conventional lathe chuck. You can use a spider instead to achieve the same effect, though often that type of spider (there are at least two other lathe tools also called spiders) only aligns the work rather than resisting cutting force.
Both could come in either independent or scroll forms, with the independent ones allowing adjustment of the work to centre it, scrolls being quicker to operate. Four jaw chucks have four jaws for holding square work, faceplate chucks could have other numbers of jaws, certainly some of the woodworking ones are three jaw.