Electrochemical insertion of Mg ions into Mo6S8 Chevrel phase is a unique, model system for studying the nature of the energetic inhomogeneity of the host sites suitable for ions accommodation. We show that the two energy state model can be successfully used for describing the very specific Mg ions insertion kinetics into the host, in particular, as relates to a drastic increase of Mg ions mobility in the vicinity of the critical potential of 1.25 V (vs Mg). This is accompanied by very pronounced changes of the impedance spectra. On the other hand, similar behavior of impedance spectra could be obtained for geometrically nonhomogeneous intercalation electrodes, comprising a distribution of thicknesses. One can frequently meet both these cases in practice for a vast variety of intercalation electrodes (e.g., for lithiated graphite, composite Li(x)MO2, M = Mn, Ni, Co, etc.). In this paper, we developed a methodology aimed at a reliable distinction between the two alternatives, based on complex impedance and complex capacitance analysis.