To me, pare means to remove the unwanted parts (potato skin, rotten parts, etc). Peel simply means to remove the outer thin layer of vegetables and fruits
:up: In order for you to peel something, it has to have a peel! But even after you peel a vegetable you may want to pare a bit off.
But 'pare' isn't very common as a verb. Depending on the shape I was cutting I'd say slice/chop/dice. But 'paring' is more common in compound words: "cheese-paring" or "paring-knife" for example.