We know that Wigner crystal is a crystal formed due to interaction(kinetic energy is quenched). It is a crystal of electrons and therefore has periodical oscillations in the charge density. Therefore it seems it is legitimate to call it a charge density wave as well.
However more often than not, the charge density wave(CDW) emerges as an instability from some free band electrons, when the interaction is added. In this picture, the electrons that constitute the CDW can move freely(when the CDW is formed, they subject to the CDW potential scattering.)
So the question is: what are the key differences between Wigner crystals and CDWs? When are they interchangeable, if possible? Or they are two extreme descriptions of the same thing, similar to the band theory case where a problem can be described by either the Bloch wavefunctions or the Wannier functions(it is just a matter of good starting point for a particular problem.) It seems to me the answer is yes. But I am not quite sure about it.