A cheese toasty is layer of cheese melted between slices of toasted bread. Any cheese is used (usually cheddar) and it may be mixed with things like onion. It is eaten like a sandwich
A rarebit is a single layer of thick bread generously topped with a thick. cheese sauce rather than plain cheese and eaten with knife and fork. Most recipes contain a splash of beer so you have to drink the rest.
Finally if you're the type who thinks leaving a cheese toasty open and sprinkling it in Worcestershire sauce makes it a rare rarebit shame be upon you