 Both groups have a shell consisting of two valves , but the organization of the shell is quite different in the two groups . In brachiopods , the two valves are positioned on the dorsal and ventral surfaces of the body , while in bivalves , the valves are on the left and right sides of the body , and are , in most cases , mirror images of one other . Brachiopods have a lophophore , a coiled , rigid cartilaginous internal apparatus adapted for filter feeding , a feature shared with two other major groups of marine invertebrates , the bryozoans and the phoronids . Brachiopod shells are often made of calcium phosphate as well as calcium carbonate , whereas bivalve shells are composed entirely of calcium carbonate . 
