Yeah but slightly different if you use a dedicated toastie maker which are pretty common, it seals the bread around the edge and gives you a perfect pocket of cheese.
That's why you intentionally overfill the sandwich so that when you press down on the maker some cheese is hanging out the side, and the rest gets trapped in its pockety goodness.
I looked up "grilled cheese sandwich maker" and apparently there's quite a few kinds as well. Personally I prefer a small nonstick pan because I like the overflowed cheesy goodness. My dad would sometimes make us "iron cheese sandwiches" by wrapping them up in aluminum foil and putting the hot iron on top. They were really good, but with a tendency to scorch, and sometimes Mom got mad if butter leaked out onto the ironing board. He'd use Longhorn Colby cheese in thick slices of my mom's homemade bread.