Like is said above: 'gonna' and 'wanna' is an example of English slang. It is grammatically incorrect and improper in formal situations. 'Gonna' is a contraction of 'going to' and 'wanna' is a contraction of 'want to'. The same goes for these words: 'Imma' = I am going to 'Gotta' = have got to 'Kinda' = kind of 'Dunno' = don't know 'Shoulda/coulda/woulda' = should have, could have, would have 'Oughta' = ought to 'Lemme' = let me 'Gimme' = give me 'Lotsa' = lots of etc. etc. etc. I hope I could add something to the comment made above, which was already clear enough.

"gonna" and "wanna" are casual, slangy ways of saying "going to" and "want to." Sometimes "wanna" is used to be whiny, usually by small children (example: "I wanna go too!") You can use them in very casual conversation, but I would recommend steering clear of these phrases for the most part. It's not proper english, so don't use them in situations where you need to be taken seriously.

Yes, as already noted, wanna and gonna are forms of want to and going to. It's common for English people, when they are speaking rapidly, to drop the unstressed part of the word. Although you don't need to aspire to speak like this when you learn English, you should learn to recognise these words (and others) to help you with your comprehension. Hope that helps!

Thank you