For a person far from martial arts: MMA is a type of martial arts, mixed style, if in simple language, where both striking technique and wrestling techniques are allowed. UFC - mixed martial arts federation.
MMA is a sport, and the UFC is just a championship in this sport. More details are written in this article: http://mmation.com/mma/chem-mma-otlichaetsya-ot-ufc/
MMA is a sport.
UFC, Bellator, M1, Fight Nights, WSOF, One Championship, ACB are all organizations that conduct fights according to the rules of MMA. If we draw an analogy with football, then there is the sport of football and there are organizations FIFA, UEFA, etc.
MMA is an abbreviation for Mixed Martial Arts or mixed martial arts, which in Russia is often incorrectly called "ultimate fighting". The rules are there, and they are strict, it is just that the fighters are allowed a lot more action than in traditional martial arts. In other words, MMA is a sport.
UFC - Ultimate Fighting Championship (Russian Absolute Fighting Championship) is a sports organization that holds tournaments according to MMA rules. This is a typical commercial company, the head of which, Dana White, makes millions of dollars from advertising, broadcasting, selling UFC-branded goods and so on. There are many organizations that are doing the same, just less is known about them, for example, Bellator, Strikeforce and even the Russian M-1 Global, the main locomotive of which was our fighter Fedor Emelianenko.
I understand your question in the sense that people often associate MMA with the UFC as the most popular brand. But the UFC is just a special case in the world of MMA.