Here's the thing. You said a "melt is a grilled cheese." Is it in the same family? Yes. No one's arguing that. As someone who is a chef who studies sandwiches, I am telling you, specifically, in culinary school, no one calls melts grilled cheeses. If you want to be "specific" like you said, then you shouldn't either. They're not the same thing. If you're saying "cheese sandwich family" you're referring to the taxonomic grouping of Queso, which includes things from cheeseburgers to tuna melts to quesadillas. So your reasoning for calling a melt a grilled cheese is because random people "call the cheesy ones grilled cheeses?" Let's get tacos and cheesetoast in there, then, too. Also, calling something a brie or an camembert? It's not one or the other, that's not how taxonomy works. They're both. A melt is a melt and a member of the Queso family. But that's not what you said. You said a melt is a grilled cheese, which is not true unless you're okay with calling all members of the queso family grilled cheese, which means you'd call cheeseburgers, tuna melts, and other sandwiches grilled cheese, too. Which you said you don't. It's okay to just admit you're wrong, you know?