Charge density waves (CDWs) arise from the interplay between electrons and lattice distortions and are a hallmark of low-dimensional systems. Here we study coupled Su-Schrieffer-Heeger chains, both lattice-matched ladders and lattice-mismatched moiré superlattices, and find a rich set of CDW phases together with symmetry-protected bound states. In lattice-matched chains, the competition between electron-phonon coupling and interchain tunneling drives a sequence of CDW phases, including staggered dimers, trimers, and incommensurate states. These phases are generally gapped and host bound states protected by crystalline symmetries rather than chiral symmetry, and are therefore not pinned to zero energy. Lattice mismatch further reconstructs these phases into long-period supermoiré CDWs, with an ordered array of defects, pinned to the moiré length scale, that host localized electronic states. Interchain tunneling and lattice mismatch thus emerge as natural control parameters for CDW order and bound states in one-dimensional chains.