Wedding Band: A ring worn on the ring finger of the left hand signifying that the wearer is married. Use this tag when the ring is simple, such as a standard gold band.
Wedding Ring: A ring on the ring finger of the left hand, or a ring that is otherwise obviously a wedding ring (e.g. post #213506). Use this tag when the ring is intricate somehow, such as having a gemstone.
Also, my previous statement was unqualified; I just have a vague recollection of seeing the two tags mixed up.