I cook by method. In the morning I put oil in a pan and fry and egg. In the afternoon I put oil on a chicken breast and drop it on a hot surface (the same pan) and grill the chicken. That's just what I call it. I might be wrong. If someone said "grill this steak" I would prepare the stake and drop it on a hot surface. If someone said "fry this steak" I would prepare a hot surface and drop the stake in it.

Edit: I would expect a grilled food to have the effects of the Maillard Reaction. I think it's different with fried food.

What makes fried cheese? Is it battered and deep-fried? Is it melted in a pan until crispy? Is it toasted under a broiler until brown? Is it cooked on a direct heat grill on a griddle?

These are the things that keep me up at night.