Going to /ˈɡəʊɪŋ tə/ (UK), /ˈɡoʊɪŋ tə/ (US). It is the full form; gonna /ˈɡə.nə/ (UK), /ˈɡɑː.nə/ (US) is the informal spelling of how it is often spoken.
She's going to call you. In connected speech the vowel of to reduces to /ə/, and this reduced sound plus the weakened first word is what gonna mirrors.
We're going to be late. Spelled as two words, with going keeping its full /ˈɡəʊ.ɪŋ/ sounds. In relaxed speech, though, going to often reduces to /ˈɡə.nə/ (UK) or /ˈɡɑː.nə/ (US), which is why the informal written form gonna exists.
What are you going to do next? In relaxed speech this often sounds like /ˈɡʌnə/, which is why the informal written form gonna exists.
Gonna /ˈɡə.nə/ (UK), /ˈɡɑː.nə/ (US) is informal register: fine in texts, chats, and dialogue, but avoid it in essays, emails to strangers, or formal writing, where the full two-word spelling going to is expected.
Watch the spelling traps: the word is going, with o-i-n-g, so goign swaps two letters and goiing doubles a vowel that is spoken only once as /ɪŋ/.
Gonna is transcribed /ˈɡə.nə/ in British English and /ˈɡɑː.nə/ in American English, and that spoken shape is what justifies the spelling. In fast speech, the vowel of going weakens and the word to loses its full /uː/ and reduces to /ə/, so the two words run together as this single casual form on the page.