For a weak electron-phonon coupling, the CDW state manifests itself mainly around the Fermi surface, and thus has definitive coherence length. This type of CDW transition opens up a bandgap around \(k_f\) and is called incommensurate. However, a stronger electron-phonon coupling is fundamentally different in that it will change the electron bandstructure entirely, and offset the entire electron band while also dramatically changing the dispersion. Thus, it will have a definitive superlattice but will not have a well-defined coherence length. In a very simple sense, these two facets are the two opposites of a Fourier-domain argument.