A comparison is made regarding the derivation and the results of two approaches known from the literature that aim at the current-voltage relations for ions and electrons as well as the spatial charge or conductivity distribution in a mixed ionic-electronic conductor. As a result, the relationships that were published some time ago are revealed to be completely equivalent to the outcome of the classical theory of Wagner including the extensions put forward by Choudhury and Patterson. With respect to practical use, the formulas according to Wagner, Choudhury, and Patterson even have a somewhat higher information content than the relationships emerging from the more recent approach.