freeze vs push
The direction of the wave. Freeze keeps it on your side, push sends it to theirs. Both are choices, and the wrong one costs a lane.
freeze
Freezing is holding the wave near your own tower by killing only what you strictly have to. The enemy has to walk up to farm, and so expose themselves to a gank, or give up their gold. It is the strategy of the player who has the lead and wants to keep it without risk. "freeze the wave", "just last hit".
open the page →push
Pushing is killing the wave fast so it moves towards the enemy tower. You push to back without losing minions, to take a tower, or to go help elsewhere. But a pushed wave is a player far forward and alone: pushing exposes you. "push then b".
open the page →Why they get mixed up
Both get asked of the jungler and the laner in the same words, and many players push on reflex when they should have frozen. The question to ask is always the same: where will the enemy be when the wave gets there? Near their tower, safe, if you push. Far from it, in reach of your jungler, if you freeze.