Top lane slow push vs fast shoving

This question might get much deeper into lane states, but could someone explain to me the advantage of slow pushing vs hard shoving. Correct me if I am wrong, but slow pushing is when the opposing planer is not in lane, the wave is on your side (and isn’t frozen), you last hit that wave then hard shove the next to get the wave under tower

I have watched a decent amount of educational, and everyone says slow push, slow push, slow push, but I just don’t understand how the result differs from just hard shoving the same 2 waves. Could someone explain what I am missing?

Context: I’m a silver/gold level jungler who is trying to learn top and make it my main role