More lazily quoting Wikipedia. How do they act differently? They're aristocratic southern women. And I don't know any examples of southern belles in Disney movies, but there are southern stereotypes.
I'd say look up The Princess and The Frog, if you want Disney movies, or maybe even Song of the South. But Song of the South is widely regarded as being racist. Besides, southern belles are, for the most part, a thing of the past.
I'm only talking stereotypes and cultural this though, because, in essence, the whole world is the same without that. In all honesty, the south is no different from any other location on the Earth. But the people are, culturally different. There is not 'rest of the US' because every region developed it's own culture. They may be similar, but definitely not the same.