They both mean the same thing, though the first one is colloquial - slang. It should be avoided until you have mastered the language. It comes from the Southern and Western US dialect. "Real" is truth, actuality, or quality of being proven. So "really" mean truthfully. "Really" is an adverb that enhances the adjective "pretty" to make it more powerful. You would enhance an adjective with "really" in order to sound more honest when stating an opinion. It also, however, shares a meaning with "very." "You're really pretty," "That's really dumb," and "This is really the worst time I've ever had" are all correct uses.

I agree with Jkduzz - "It's real pretty" makes you sound like a cowboy. (You could probably pronounce "pretty" as "purdy" if you want the full effect!)

there is no difference- real is a regional dialect of really

Well, if "real" is a noun and "really" a adverb, I actually thought there's a huge difference between this terms. "It's really pretty" refers more to intensity of prettiness and "it's real pretty" to veracity of beauty I guess.

Your second question should read: "How do you use "real" and "really" in different situations?" to be more proper.