On the Food network they boil potatoes, but they poach carrots. They poach turkey, but they boil eggs. They sauté’ onions, but they fry eggs in the same pan. Likewise, they fry hash browns, but they sauté’ onions in the same pan before adding the potatoes.
I can go on for days.
I have noticed many people from outside the US get hung up on grilled cheese. We just call it that for some reason and no one really thinks about it. If we stop to think, we know it is not grilled, and as far as I’m aware, it’s the only thing we call “grilled” that is not grilled. I think the reason we do not call it a toasted cheese sandwich, or cheese toastie, as I think I’ve heard in the UK, is that would imply the use of a toaster (a standalone appliance with electric heating elements inside slots just big enough for a single slice of bread). I suppose griddled cheese might be a more accurate name, but we are too far gone to make that change.
Grilled cheese is cooked on a flat top grill/griddle, most people use a pan in home cooking because they don’t have a flat top or it’s just easier for a single grilled cheese to use a pan. Reubens and paninnis are other sandwiches that are grilled. You could probably argue that grilled generally means cooked at high heat. Then there’s pancakes which are more commonly cooked on a griddle than a pan…
There’s a few different things here that make clarity difficult. One is the precise definition of various techniques, for example:poaching water is not bubbling, simmering water is gentle bubbles, boiling water is bubbling heavily(some say “full rolling boil”, which is what boiling always is. Second is simply the name of the cooking vessel/equipment, griddle vs grill vs broiler, which is sometimes the same term used to describe the technique applied. You can grill a steak, but you wouldn’t say you ovened a roast. Last is that many terms are misused so much that it’s just become common parlance. Technically a grill is a device with grates and a radiant device that cooks food through a combination of conduction and radiation, usually powered by propane or natural gas. A BBQ is a similar object powered by wood, but it’s common for an outdoor grill to be referred to as a BBQ, though when used with the lid down is a little different than an open restaurant style grill since it acts a bit like an oven too.