Although not always the case in the past, most divers today use a buoyancy compensator (BC) to compensate for the two things that cause you to be more negatively buoyant during part of the dive (that is, the two things that change during the dive). These are the weight of the gas that you consume and the loss of positive buoyancy of your exposure suit at depth. So if you are perfectly neutrally buoyant at the end of your dive, with a near empty tank, in the shallow water of the safety stop, you will need some gas in a bladder somewhere after your initial descent to compensate for the weight of the extra gas and the compression of the suit.
That gas in a bladder is part of any BC - whether it is a jacket style or a backplate and wing system. The functional difference between the two is that the BP/W is modular and the jacket BC is one manufactured piece. With a BP/W, you have a backplate bolted to a wing (the wing is the gas bladder, a separate item). Then you have some webbing (the harness) that straps the plate and wing to your back. You also need some way of attaching the BC (backplate or jacket) to the tank. For most single tank setups, this means cam bands.
So you wouldn't get a wing by itself, it would be a part of a backplate and wing system, which would include the harness threaded into the backplate. And BP/Ws are great! See any of the many threads on them here...