Another way of dividing the different ways of gaming is to group them into gamist, dramatist, simulationist and eläytyjist styles. The gamist players ("munchkins") try to somehow win the game by making their character as powerful as possible - in a way turning the role-playing into strategy-gaming. The dramatist people have no true grasp for the meaning of interaction, as they think the purpose of the game is for the game masters to tell a story using the players as actors - but with no audience to tell the story to! The simulationists try to create a working society or even a world which is simulated through role-playing. The eläytyjist set the goal to becoming the characters, to experiencing everything through the character.Setting aside the pretentiousness for a moment, what they've done here is rather fascinating: divided roleplaying styles into four groups based on whether they focus on creating a story, overcoming (largely mechanical) obstacles, creating a world, or immersing yourself in a character, and then grouped the story and achievement styles in one category and the simulation and immersion styles in another.
While the division between the mediums of LARP and table-top games does not provide any difference in quality, the second division certainly does - not all of the above styles are as well thought-out as others. As is obvious to most role-players, the dramatist and the gamist styles are inferior to the simulationist and eläytyjist styles.
While their presentation of the idea is somewhat problematic, my thoughts have been running along similar lines for a while now. The summer that 4e D&D came out, there was a lot of talk about how it had incorporated "Forge philosophy" into its design, and while I don't know enough about Forge-style games to comment substantively, what I do know has suggested that there are some definite points of contact between those two sets: they're both using rules to engineer very specific experiences. And in that quality at least they both stand very much apart from the kind of gaming I've been doing a lot of lately, where we'll ditch the rules entirely for months at a time, and don't figure out exactly what want out of a campaign until six months into it.