Thanks, was having this discussion on the historical discord server, and we all agree on running/acceleration. and regular movement is just walking.
Making it realistic or at least the ratio between the two though start to create problems. Since running only happens in those two situations, it doesnt make sense that a horse would cover the same distance across the map only a little faster than human. You would almost need to add in stamina or something that might make it way too complex, so now just trying to find the right balance where cav mobility isnt too op, especially for civs with limited, weak cav.