There’s a lot of discussion about this all over the place. I hesitate to answer, but I would like to shed some light on some of the terminology in use and mention some bits where I think people may be being unclear.
According to the old Threefold Model, which is a seminal attempt at theoretically classifying approaches to roleplaying, there are three (natch): Gamism, Simulationism (or Immersion), and Dramatism (or Narrativism). Usually people don’t come purely from one approach or the other but some mix of them, although you usually see consistent leanings into one of the three approaches. Would you like to know more?
“Gamist” usually means a focus on playing the game for the rules, with clear challenges and victory conditions and metagame goals. Often in games this means combat, but skill and interaction events are also gamist if pursued with a “rules first” mentality. Some people like the gamist approach. Gamism is what people are complaining about when they say “D&D 4e plays like Magic/RoboRally/a board game/a tactical minis game/etc.” Gamists like to “do what will win.” People don’t use the old terms “munchkin” or “powergamer” much any more, but they were deprecating ways of referring to gamists, since they worried about their character’s build or loot more than a realistic in-game motivation.
“Simulationist” usually means a focus on “becoming” the character inside a realistic game world. RPGers like to use the big word “versimilitude,” which means “Yes I know magic isn’t ‘realistic,’ but the game world can still behave realistically according to its own rules from its inhabitants’ point of view.” Simulationists like to “do what their character would do.” Metagaming, or making decisions about what the character does using information not obvious to the character, is heavily frowned upon. D&D was extremely simulationist (with a side plate of gamist) up through 3e; a lot of the reaction to 4e is its movement in the other directions.