Your movement is separate from your action.
The differences are minuscule, and to 5E's disadvantage at that. Instead of freely assignable action pool representative to your character's time share in combat round, you have:
1 AP) a dedicated movement pool that gets pretty much wasted if unused, which is ridiculous.
2+ AP) bastardized action pool (if you have bonus actions), that can be spent only on single quantified activities like attack or bonus move.
Systems like that are OK for P&P because they're there for their simplicity to be resolved by humans. Plus GMs have infinite capability to interpret player's declarations according to common sense. But P&P RPGs don't equate cRPGs, which have always had their own way of presenting combat because it's trivial for a machine to represent more numerically complex systems like AP proper. With regular action pool the control over characters is much more precise and allows virtually any combination of actions, taking things like turning or varied attack times into consideration. In fact both RTWP and proper TB are superior to that, because both allow more complexity. Simplification is the steeple of decline.