They mean the same thing but "have" is grammatically correct. You'd see this in books, hear this in speeches and see this in the writing of assignments. "Got" is more casual / slang / everyday speech. You'll hear this on the street, on a bus, from kids and in daily informal conversation.

Nothing. I have = I've got (but not always).

Hi! This is a good explanation. Check the site. =) I hope it helps, you also have some examples and exercises to practice. Good Luck! http://www.britishcouncil.org/learnenglish-central-grammar-have-v-have-got.htm

I don't like replies completely based on the Internet, this time I'll do an exception. If you don't already know what this is about, please go 'googling' with terms as: Houston, we have a problem, Bus B undervolt I know it is not exactly what you asked, but maybe you might get interested in a historical usage of these terms.

I gotta say, you have no problems. :P