Woodworking vises come in several types, all metal all wood or a combination.
I use this, all metal type and have one at each side of the bench. This allows support for longer pieces that will fit in between or shorter ones in one end or the other. I don't have wooden jaw faces, although I know that I should. It is the easiest to install:
A true woodworking vise is usually made from all wood, a wooden threaded screw,wooden faces, and wooden slides. This type has been the standard for a few hundred years and you'll see them on older joiners benches from the past. That was the material at hand and it will also protect the sharp edge of a plane or chisel IF you happen to slip. Newer versions use a metal screw and has to be integrated in the bench design from the start:
There is also a combination of metal screws and slides and wooden jaws like this. It combines the strength of metal and the protection of large wood faces and it's fairly easy to install:
So, if your bench is already built you are probably limited to the first and last types. The first version, like Steve said has a sliding vertical dog that will hold thin pieces against a dog located behind it, a good feature. You can always add brass dowels or wood to any of the wooden jaws for the same purpose.
The purpose of a woodworking vise is to safely hold all sizes and thicknesses of material for drilling, chiseling and planing. There are leg vises and pattern maker's vises that will add even more features.
There are also shop made versions: