I admit I don't have much to back that up, but I've always been under the impression that bodyglove just meant "tight fitting clothes", regardless of the actual material and/or armor value... It can refer to both "spandex-style" costumes and to close-fitting body armour (for lack of a better example, like those worn by most guys in the horrible movie G.I.Joe)...
However syn(th)skin is a material, with the same general qualities as skin, which is normally used to patch wounds (very likely the reason for which is was invented) and sometimes, in a slightly different variant, to cover one's whole body. It is sprayed on... For lack of a better example, imagine someone sprayed all over with a few millimeters-thick coat of (black) latex, and it'd be what someone wearing syn(th)skin would look like...
Thus the big difference between a bodyglove and synthskin would be the fact that synthskin sticks to one's skin while a bodyglove is merely a tight-fitting costume.