Using my rule of thumb above: if I asked the waiter for a grilled cheese, but I didn't care what kind, I expect the waiter would be somewhat perplexed by this, since "grilled cheese" is a sufficient descriptor that there's basically one sandwich that satisfies the description.
If I asked for a melt but didn't care what kind, then I feel like the possibilities expand, and would include a regular grilled cheese.
If I asked for a melt but didn't care what kind, then I feel like the possibilities expand, and would include a regular grilled cheese.