Wings and spoilers are body components used for adding downforce, and can sometimes (usually for racing purposes) be adjustable. Wings on a vehicle are just like wings on a plane, except instead of creating lift, they are upside-down to do the opposite. Spoilers, however, are usually just extentions of the body, which (although effective at creating downforce) are generally less effective than wings by creating more drag than a wing would.
Spoilers extend from the body making sure all the air moving across the surface has to flow further upwards at the end of the vehicle, forcing pressure to build up which pushes down on the back of the vehicle. Seen at the right is a carbon fiber rear spoiler on a Honda S2000. Some rear spoilers are more decorative than functional, and some race cars have spoilers due to regulations which don't allow them to use wings. Usually wings are preferred over spoilers when maximum performance is in mind, and spoilers tend to be favored on vehicles by people which like a somewhat sporty look which isn't too flashy.
Wings are positioned away from the vehicle's body so the air can flow both under and over it, like an airplane wing only upside down. Vehicle wings often have plates on the tips of the wing to both improve stability (by resisting any change in the rear angle) and to reduce wing tip vortices which reduce the effectiveness of the edge of the wing.