"Go out" usually describes some purpose, such as going out to a movie or to dinner. It usually means with a boy- or girlfriend, but can also mean with friends. "Hang out" usually means that one is just sitting with one or more friends (possibly a boy- or girlfriend) and just talking or looking. It implies that nothing special is happening - just being together. "Where are you going?" "Some friends are picking me up and we're going to just hang out at the shopping mall." "What are you doing this afternoon?" "I'm going over to my girlfriend's place and hang out there."

go out usually means date with girlfriend or boyfriend. hang out means some friends get together just for doing something relax or random,not so serious. in addition,you can say I hang out with friends at ITALKI website.