Olympic Recure is a bow with limbs that curve away from the archer when unstrung. Adding sights, weights, stabilization, etc to the bow classifies it as an Olympic recurve.
Barebow is a bow with limbs that curve away from the archer when unstrung. Just like the Olympic recurve but no sights and stabilization but weights can be added if they don't extend more than 12 inches from string to end of riser.
Compound bows use a cam system that use cables and strings. There are cam stops plus let offs that allow the archer to draw tot he same spot every time and allows them to hold more weight because there's a let off at full draw. No limits on sight, stabilization and release. There is a draw weight limit of 60lb.