To me beauty is the whole package. It describes sophisticated, sexy, loving, strong, couragous, and driven women. Of course beauty also means you are cute, but cute is on a much more superficial level.
What my boyfriend says is a girl is beautifil when he can consider to wife her. and when she's cute she's just cute she doesn't have potiental to be a wifey
I've heard that "cute" corresponds to a pretty girl with a fun personality, but "beautiful" is deeper, like an amazing girl all around (beautiful mind, face, personality, etc.) which typically comes after the guy knows you (for some guys).