The simple answer is this : NEVER. Take a look through the pages of this site. Make a note of (1) how many native English speakers (British, American, Australian and so on) who have written 'gonna' in their texts, questions and answers. (2) how many foreign learners have written 'gonna'. If you do this you will find native English speakers do not write 'gonna'. We don't write 'wanna' or 'gotta' either. It is only foreign learners who write them. Foreign learners see these forms written on subtitles, in song lyrics and cartoon captions and imagine that this is 'real' English, as used by native speakers. It isn't. It's simply a transcription of how 'going to' sounds when we are speaking in a rapid and/or casual way. We say 'I'm going to go', but it sounds like 'I'm gonna go'. Writers of songs, subtitles and cartoons use these forms to suggest fast and informal speech. So, to answer your question. 'Gonna' is not a tense. It's a shorthand form that suggests what we hear when people say 'going to'. And no, there is no difference in meaning between 'going to' and 'gonna'. The difference is that one is proper English and the other isn't. Please don't write it.

You're right! Gonna is the same as going+to, the difference is just pronunciation and context. Like you said, it's informal. When talking in an informal setting, like with friends, 'gonna,' is acceptable. When native speakers speak English, we link words and 'going to,' becomes 'gonna,' Similarly, 'I want to_______,' becomes I wanna.

I totally agree with Mannay and I have one more 'linked' and very colloquial 'word' to give you as an example: Watcha think? = What do you think?

Su Ki is absolutely correct. The use of "gonna" and indeed its terrible cousin "wanna", is just bad English. They are perhaps pardonable if written by an eight-year old. Non-native speakers, please don't embarrass yourselves, reduce your job prospects with English language employers and risk losing marks in English tests by getting into the habit of using either of these!

You can use "going to," Miguel if you are more comfortable with it. That is perfectly okay. However, I was speaking on pronunciation. Being aware of linking is necessary for listening comprehension. Reading and writing is separate. Su. Ki is correct in saying that 'going to,' is the only proper way of expressing this statement in writing. However, if we go back to the informal setting, I will text my friends "wanna go to the mall?" or "I'm gonna do that later." I am a native speaker. It's not the 'proper,' form but you will see it and hear it. Again, context is important - informal vs. formal and the age of the person you are communicating with and the relationship you have with them. Continue to practice the correct form, but also be aware of different practices. :)