These are two types of pin vises. The one on the top is a 'Swivel Head' and the one on the bottom is a Double Ended or better known as the 'standard' pin vise. Each is used in the same manner, twist one of the heads to open the inset jaws and then insert the end of a single piece of wire, (or two or three small gauged wires), into the center and twist the head tightly closed around the wire(s). Hold the opposite end(s) of the wire(s) firmly with flat-nose pliers and twist the pin vise with the other hand until the wire is twisted to the desired look. Then twist the head open to release the wire. With regards to wire jewelry creation, these units are most often used to twist shorter lengths of wire, from ¼-inch to 12-inches. Each of these two pin vise styles can be used to twist separate segments on the same wire, (as the swivel head is removable). This is done by either opening both ends, or by removing the end opposite that which is to hold the wire, and inserting a longer length of wire through the entire pin vise, so only a short length is protruding from the tightened end. Hold this end with flat -nose pliers and twist to desired effect, then open the tightened end and slide the untwisted wire through to the desired length, hold that segment where desired with flat-most pliers and twist the part that is between the flat-nose pliers and the tightened end of the pin vise. Repeat the procedure until the entire wire length has been twisted in whatever segments are planned. For example, a 12-inch wire could be twisted every other inch and then used in the planned design. Either pin vise will work to twist a single wire up to a 16g. When either pin vise is used to twist multiple wires, the best results happen when using no more than 2 wires at a time, in gauges 22 and smaller. Most often, either of these units is used to twist a single wire.
My personal opinion: The only benefit to owning either of these styles of pin vise is in having the option of twisting certain segments on a single wire. Each is small, compact and can be traveled with easily. As for twisting single wires when embellishing a design, it takes a bit of time to unscrew the head, inset a short segment of wire, screw the head tight around the wire, twist a few times and then unscrew the head to release the wire.