Cute = comment not to be taken too seriously, still attracted but not wanting to commit to it "Yeah she's cute"
Beautiful = really good looking, but reserved for special occasions or to combat your self-doubting "Don't worry about it, you're beautiful!"
Pretty = the nice in-between. likes you enough to want to say something more than "cute", but thinks it might be creepy to call you beautiful, or that you might think if he did say that word instead, that you think he's just using a line on you. Another version of pretty would be saying "You look good!" or good-looking, etc.
Cute I have always seen as something that describes not only your physical appearance but personality as well (if someone says 'you're cute' directly to you)
Pretty is purely physical. It is similar to hot but describing a different kind of person. Hot is usually associated with the more bold and wild girls while if you are described as pretty it probably means you have a more natural and under-stated physical beauty.