Brachiopod shells are quite different from bivalve shells, and the living creatures within are very different. Both shells can be cut into two identical halves that mirror each other. Whereas the mirror plane in bivalves cuts between the two shells, the plane in brachiopods cuts each shell in halfit's vertical in these pictures. A different way to look at it is that bivalves have left and right shells while brachiopods have top and bottom shells. Another important difference is that the living brachiopod typically is attached to a fleshy stalk or pedicle coming out of the hinge end, whereas bivalves have a siphon or a foot (or both) coming out the sides.
The strongly crimped shape of this specimen, which is 4 centimeters wide, marks it as a spiriferidine brachiopod. The groove in the middle of the one shell is called a sulcus and the matching ridge on the other is called a fold. Learn about brachiopods in this lab exercise from SUNY Cortland.