How to tell a girl that you want only to stay as friends?

You're comparing two entirely different scenarios. No one that isn't in a relationship would walk up to a guy and say "Want to sleep with me?", if a girl did that, it's evident she's a whore, and the guy would have to be either drunk, outrageously horny, or has no sense of right and wrong.

I thought cuddling was something only people who are in a relationship do. I guess I'm more out of touch with social norms than I thought.

By the way, I didn't mean sleep as in sex, I just meant sleeping with each other in the same bed cuddling together.