Brachiopods differ from bivalve molluscs because their shells are
Both Brachiopoda and Bivalvia display superficially similar bivalved shells leading to historical confusion yet fundamentally differ in symmetry, orientation and anatomy. Brachiopod valves occupy dorsal and ventral positions, inequivalve, plane bilateral symmetry bisecting each valve medianly, valves not mirror images. Bivalve valves are left and right lateral usually equivalve mirror images with symmetry between valves. Brachiopod shell may be chitinophosphatic or low-magnesium calcite punctate, unlike nacreous aragonite typical bivalves, reflecting independent evolutionary origin of shell se
Ref: Brusca & Brusca, Chapter 22: Brachiopoda vs Bivalvia dorsal ventral valves orientation