AnnaOnTheMoon, I know this is probably going to be way more conversation on grilled cheese than you really wanted but:
http://talk.uk-yankee.com/index.php?topic=38116.0
And yes, no doubt I'll be wanting a 'grilled' (sauteed?) cheddar sandwich and tomato soup for lunch now. 
hehehehe Right. See, and this is why we should *always* click the "search" button first. *shakes head* Feel free to dunce cap me.
What about Monte Cristo sandwiches? Are they an american thing only? Those are my FAVE sandwiches EVER!
I'm a vegetarian, so I don't eat them, but what really confused me when a friend of mine ordered it was the powdered sugar and pancake syrup it came with.
To me, "fried" implies that at some point in the process the food was at least partially submerged in hot fat/oil - which grilled cheese sandwiches are not, even when made in a frying pan. I agree that they're not strictly "grilled" either, though.
I believe the term *may* have evolved dialectically, at least in some circles - my great grandmother always referred to them as "griddled cheese" and my family's always made them on a griddle pan rather than in a frying pan (with a minimum of butter - just enough so that the bread browns evenly).
*nods* we sometimes use a griddle pan as well, but Tim didn't know what a griddle was, so I called it a frying pan. I don't think Grilled Cheese is fried when you make it at home because you're controlling how much butter you use and what's on the pan, wheras I might be able to be convinced that Grilled Cheese from a diner type restaurant is actually fried because often those do come dripping in butter.
When I make it the US way, in a pan, I can never get the cheese to melt properly unless I let the bread go almost black. Is there a trick to it?
I know it's already been suggested to use less butter and less heat, but also if you flip it more often it will brown evenly. I also sometimes use butter flavored cooking spray instead of butter and it works pretty well.
On the fried vs. grilled front, I think a lot of that has to do with the way you cook it and what you put in it. Using lots of real butter will up the fat content, but when you use margarine or spray it can make it a bit healthier, and if you use low-fat cheese.