Slashers are definitely... their own subgenre. And one that can be pretty damn stupid, haha. It's not my favorite subgenre, though it is true that they've had a pretty strong effect on a lot of modern horror, too. It can be interesting just to see where some of the common tropes and things come from (or at least where they became sort of codified.)
I liked Nightmare on Elm Street I think because the supernatural element is stronger. It's also present in the Friday the 13th franchise, though not quite as overtly, at least initially. By contrast Halloween has the implication of a somehow supernaturally unkillable killer, but for the most part it's much more mundane.