Two gas dynamic analytic approaches [of a Burnat type / Martin type] are respectively used in order to construct two analogous and significant pairs of classes of solutions [isentropic pair / anisentropic (of a particular type) pair]. Each mentioned pair puts together a class of “wave” elements and a class of “wave-wave regular interaction” elements. A classifying parallel is finally constructed between the two analogous pairs of classes -- making evidence of some consonances and, concurrently, of some nontrivial contrasts.