Two sides of a polygon that share a common endpoint are called consecutive vertices

No, that's not correct. Two sides of a polygon that share a common endpoint are not called consecutive vertices. They are called adjacent sides. The points where the sides meet are called vertices. If two vertices in a polygon are endpoints of the same side, they are called adjacent vertices. Consecutive vertices, on the other hand, refer to vertices that are connected by a single, straight path (or edge) in the order they appear in the polygon.