Part of this is just terminology, but I stumbled over this naming, something this TKD guy lables a "sword" kick, like a hybrid between ushiro mawashi geri and axe kick, that is is getting closer to my preferred power version of ushiro mawashi...
Except I don't use the edge of hte foot, I used the heel, so it's like a hammer instead of sword, but having both a slight forward + downward thrust as compare to the pure horizontal ushiro mawashi geri. I think this version is more robust for body kicks, and the "classic ushiro mawashi" seems optmized specifically for hitting the jaw (without stopping).
Its amazing so see that all the off-standard or perso nalized versions of kicks actually have their own names in other styles.