My cousin asked me to clarify the difference between the various MMA terms and organizations, and I ended up writing a small primer. I figure I might as well drop it here, too. Enjoy it if you need it!
 

So, mixed martial arts is the name of sport. It’s analogous to football or soccer. Players in mixed martial arts are called mixed martial artists.

There’s various fighting promotions, which correspond to sports leagues. The Ultimate Fighting Championship (UFC) is the biggest and generally most prestigious one. They’re serious about building a reputation for providing the best pure mixed martial arts competition. It’s like the NFL of mixed martial arts.

The UFC used to have a big rival in Japan called Pride Fighting Championships, but they were bought out and dissolved by the UFC. They also bought the WEC (World Extreme Cagefighting) but have kept it around to focus on the lighter weight classes that the UFC doesn’t has, like featherweight and bantamweight. People think of fights between the largest guys as being the most exciting, but lighter guys are faster and more agile, and there’s generally way more action in the lighter weight class fights.

So, there’s also promotions independent of the UFC in the US, like Strikeforce, King of the Cage, and Affliction. They tend to either be more “minor league,” featuring fighters that don’t have enough experience to be signed by the UFC, or “masters league” and have guys that are past their prime but are still a big draw.

However, they also have the occasional fighter that could beat a lot of guys in the UFC, especially among the heavyweights. These guys usually have a problem with the UFC’s really stringent exclusive contracts, which are the what they use to build up their brand. Among other things, this has resulted in Fedor Emelianenko, widely considered the best heavyweight in the world, not being able to fight the UFC’s big heavyweights.

And then there’s the Japanese promotions like DREAM and Sengoku. They (naturally) cater to Japanese sensibilities. The Japanese are usually as interested in seeing “what would happen if this guy fought this freakish guy?” than “who is the best fighter?” They end up with kind of stunty fights involving not very skilled giants like Hong Man Choi and Bob Sapp or celebrities like Jose Canseco but also a lot of legitimately competitive fights in the lighter weight classes.