"wanna"; want to; is more used for things that you wish you could do; or that you plan to do but are not 100% definite about. - "I wanna be a popstar", "I wanna go to the beach tommorow" "gonna"; going to; is more for definite plans, or to say that you intend to do something in the near future. - "I'm gonna leave", "I'm gonna be 25 next year". Both are slang, and informal speech. You should avoid using in writing or polite conversation, but chatting with friends is fine :)

Wanna is short for 'want to' and gonna is short for 'going to'