Simply put, a bevel is the angle that results from two meeting surfaces. A bevel cannot be at a 90° angle, but all other angles are acceptable as bevels.
A beveled edge refers to an edge of a structure that is not perpendicular to the faces of the piece.
A bevel is typically used to soften the edge of a piece for the sake of safety, wear resistance, or aesthetics; or to facilitate mating with another piece.