Symmetry is the key to distinguish charge density wave (CDW) and other charge modulations.
CDW is not just a wavy pattern in the charge density as literally indicated by its name, it is an order that spontaneously breaks the translation symmetry. Note that the symmetry must be spontaneously broken but not be broken by hand. This means that the Hamiltonian of the system is translational symmetric, but the resulting ground state is not symmetric (due to the density modulation).
According to this criterion, Friedel oscillation is not a CDW state, because the Hamiltonian for Friedel oscillation includes a charge defect, and this defect breaks the translational symmetry explicitly on the Hamiltonian level, so the consequent charge modulation is not spontaneous, and therefore can not be called a CDW. Also the uneven charge distribution due to the multiple atoms in a unit-cell also does not qualify for CDW, because the atoms also breaks the translation symmetry on the Hamiltonian level explicitly, so the charge density modulation is not spontaneous.
Because the CDW state is by definition a spontaneous symmetry broken phenomenon, so it can not be smoothly connected to the high-temperature symmetric state, and a phase transition (like Peierls transition) is necessary before entering the CDW phase, as it is impossible to break the symmetry spontaneously without going through a phase transition. If a charge density modulation is not associated with such a transition, it will not be a CDW state.