The Toastie question

Just what is a toastie? Some debate has arisen here at the flat as to the actual composition of a toastie, not including fillings, which is a whole sub-genre of conunderum altogether and beyond the scope of my expertise. Bonus question: What is the fundamental difference between a toastie and a toasted sandwich? There are two main camps:

1. The stance held by my esteemed flatmate J.H. who purports that a toastie is a single slice of toasted bread with a topping (usually Colby* cheese and Marmite** in his case), and that a toasted sandwich is similar, but involves another slice of toasted bread on top to make a sandwich. Logical, yes, but correct?
2. The position taken by myself whereby I suggest that a toasted sandwich and a toastie are one and the same, and that the open-topped single slice with topping (just Tasty cheddar*** cheese, in my case, although I have been known to frivolously throw some diced onion into the fray), is known as Roasted Cheese. Technically I admit it really should be called Grilled Cheese as per the method of preparation, but (in my family at least) it has always been known as Roasted Cheese.

*Read:tasteless yellow plastic cheese.
**This is allegedly a yeast extract, whatever that means, but I know that it's really tar residue scraped from the boots of roadside maintainence crews.
***The only true cheese. You know it makes sense!

What say you, good and noble citizens?