For some girls, there's a difference, but I think that most girls don't really draw a distinction. Whatever vocabulary a girl learns, she goes with that.
A lot of girls I know won't say that a guy is handsome because it sounds too serious--like she is too into him. Other girls won't say, "hot" because they feel uncomfortable about seeming to be so sexual in front of their friends--they wouldn't want to be accused of being slutty.
Most girls I know use "cute". Pretty much everyone thinks it is OK to call someone cute. It doesn't sound overly sexual. When girls are with their friends, or when they get older and more confident, or when they live in a place where people expect girls to be highly sexual, then they are more likely to use "hot".
Hot refers to the way you feel when you look at them. Physical turn on. Doesn't mean a desire for relationship, but there's a definite attraction.
Handsome is someone who is confident and carries himself well. I see this more as their personality reflected through their actions. A guy can be both hot and handsome at the same time, but if I had to pick, I'd definitely go for handsome.
Cute is more of an open feeling. When I like someone, and everything about him makes me happy, he’s “cute”. For example, I notice his habits, and every movement, and can follow his thoughts to an extent (but of course I want to know what he’s thinking about.) Someone who’s cute has emotional value – he’s the kind of guy I’d actually want to stick around.
…But sometimes cute is just if there’s some definite turn-on, but I don’t know him well enough to know his personality. The key is that I want to GET to know him.