The Threefold model of RPG systems and gameplay
There's been a lot of discussion and confusion regarding RPG systems and whatnot on the AEGIS mailing list. I've actually had to read through a more complex explanation of the Threefold model of RPG systems elsewhere, and here's what I've gotten (from a site that specializes in game definitions).

Gamist/Narrativist/Simulationist

The common name for the theory of roleplaying motivations propounded by Ron Edwards, GNS was originally presented in his article "System Does Matter" at Gaming Outpost, reprinted in the text of The Sorceror RPG and preserved at The Forge web site. Initially built on the Threefold Model, it changed the name of the Dramatist to the Narrativist to avoid confusion with Jonathan Tweet's identified Drama mechanics concept. However, proponents of the Threefold model claimed that the Gamist, Narrativist, and Simulationist categories he defined were distinctly different from those of their model.

The model has been modified, clarified, and extended such that the gamist/narrativist/simulationist aspect (now called Creative Agenda) is presented as the link between the social interaction of the players and the events within the game.

The Threefold model applies the term strictly to decision points in the game, while the GNS model uses it more broadly, and applies it to elements of game design. It is commonly used to apply to gamers and games. By some definitions, both gamists and dramatists are just sub-categories of the simulationist.

Threefold (proper n.), also Threefold model, Three-fold.

A theoretical model that classifies the decisions made in roleplaying games along the dramatist, gamist and simulationist axes.

While the formal model only applies to decision points, and not tendencies or patterns of behavior, it is commonly used to classify both role-players and roleplaying games, often in a negative fashion. This runs contrary to the original model, which is intended to demonstrate that there are different, but equally valid, ways to roleplay.

Gamist (n., pl. gamists), also gamism.

Someone who makes a decision in a roleplaying game based on what will make the most effective challenge.

The gamist belongs to one of the three axes of the Threefold and the GNS models, along with the dramatist (or narrativist) and the simulationist. The Threefold model applies the term strictly to decision points in the game, while the GNS model uses it more broadly, and applies it to elements of game design. It is commonly used to apply to gamers and games.

In contrast to a dramatist, the gamist has a tendency to "let the dice fall as they may", and won't fudge things to ensure that the player characters win. In contrast to the simulationist, the gamist has a tendency to ensure that encounters are a fair match for an adventuring party, instead of basing them entirely on what would be realistic in the setting.

Dramatist (n., pl. dramatists), also dramatism.
Narrativist (n., pl. narrativists), also narrativism.

Someone who makes a decision in a roleplaying game based on what will make the most dramatic story.

Dramatists / Narrativists often favor metagame mechanics to ensure that dramatic things happen. This can include preventing character death or giving bonuses based on how well the player describes an action.

Simulationist (n., pl. simulationists), also simulationism.

Someone who makes a decision in a roleplaying game based on what would really happen in the world.

Simulationists usually enjoy exploring the world or the setting. They are world-oriented, and frequently have high standards of realism or versimilitude to help sustain the suspension of disbelief.