I am a member of this dialect community. More specifically, I'm a member of one of several communities that use (and differentiate between) "fixin' to" and "gonna"; this bit of dialect entered American English in the South, and spread to other parts of the country during various diaspora. I lived in the deep South (in a heavily African American portion) during ages 0-3, then 9-18, so it's as close to my native tongue as it gets for me.
There are two main differences between "fixin' to"/"finna" and "going to"/"gonna". The first and biggest is immediacy: "I'm fixin' to make myeslf a sandwich; you want one?" vs "I'm gonna make myself a sandwich when I get home." "Fixin' to"/"finna" is something that you are just about to start doing, whether it's a quick process ("I'm finna grab a beer") or a slow process ("I'm finna buy that house, soon as I can get the realtor on the phone"). "Gonna" implies no immediate action, although it doesn't rule it out either: "I'm gonna retire to Destin."
The second difference is formality. Southerners do (or at least almost always eventually learn to) switch between dialect modes, and can go into formal mode when the situation calls for it. "Gonna" is simply how the words "going to" sound, when spoken in the appropriate accent; it's neither intrinsically formal nor informal. "Fixin' to"/"finna" however, is always informal. You'd use it with friends and peers (or when a fight is fixin' to start) but probably shouldn't use it when meeting disapproving parents or asking your boss's boss for a favor or doing a college interview. If you did, they'd probably understand and graciously ignore it, but they'd certainly notice and their estimation of you might go down.
ETA: "Fixin' to"/"finna" can also be conditional or dependent: "I'm finna get a hot dog, after this club" means that immediately after leaving the club, that person will seek out and get a hot dog. Additionally, both terms can be used together: "If you don't get up out my face, it's gon' be finna be a fight up in here."