Returning to my "game-(design-)purposes" taxonomy and some of the input
@clearstream and others have given, but starting (almost) from scratch in terms of examining and presenting it...
A designed thing, especially a designed thing with rules, must have a goal, an end. Laws and rules, as part of their very nature, are teleological. They must point toward a goal or purpose, and should they produce results genuinely counter to that goal or purpose, they not only can but should be changed until they meet their purpose. The process of designing anything is, in part, the process of figuring out what tools will accomplish the chosen end(s) effectively, learning what standards or functions those tools can serve, applying those tools and functions toward that end, and then checking to see whether the designed thing does the task or meets the standard of judgment for the purpose that it was created.
My interest, with this taxonomy, is to consider the families of "purposes" that roleplaying games may be designed to pursue. As a result, this is a descriptive effort, though in being descriptive I am not opposed to the possibility of finding a lacuna that can be filled with a theoretical not-widely-grokked option. As this is concerned with the overall reason for why someone would make a given game, rather than the specific methods that would work well for a given "overall reason why," individual techniques may certainly be an interesting side or follow-up discussion but are not strictly my area of focus. Furthermore, as my focus is on the thing the designer "sets out for," it is not strictly interested in things that would motivate players to choose to play the game, even though player motivation is absolutely an important and valid aspect of game design.
Having reflected on others' models, in particular Edwards', and on my own experience with roleplay, I have come to the conclusion that most "game-purposes" define some kind of central concept(s) that will drive the interest or focus of play, and then some general category of action that will constitute the process of play (from a design perspective—that is, what might be called the "gameplay loop," which is distinct from the literal lived-through process of play that actual players experience, in the same way that a blueprint differs from the physical object it generates.)
I have seen, both in games I have personally played and in the ways others talk about games whether or not I have played them, at least four distinct "game-purposes," that I choose to label with an "X-and-Y" (or, abbreviated, X&Y, just the first letters) format. These are as follows.
Score-and-Achievement. This is "game-purpose" in arguably its most literal sense, making a roleplaying game in order for it to be a game, with points or grades or numerical/evaluative testing of some kind, balance, difficulty curves, etc. A really ultra-pure S&A game is centered on that process of mastering the rules and then engaging in their skillful use in ways that matter to the player(s.) Few games are quite
that purely S&A in design, though,
"
Score" refers to the designer-created system or structure that allows at least partially objective measurement or evaluation of performance within the Situations the system considers. A game that includes Score, in general, needs a concept of "fairness" in order for that Score to be valid and worthy of player attention, and needs to not play fast and loose with the game rules so that the Score can retain relevance as a metric of
evaluation and not just a random number or keyword. Score also, generally speaking, benefits from clarity, both in the sense of "transparency" (it is easy to see how the rules work and interact) and specificity (the use of keywords and other unambiguous terms/"jargon.")
"
Achievement" is the action, by players, of pursuing success in goals, where that success can be measured or evaluated via the already-defined Score. I specifically call this "
Achievement" rather than something like "striving" or "attempting" because S&A design specifically emphasizes a focus on success, with failure pretty clearly seen as an undesirable state, something to avoid or correct, which is generally not shared with the other "game-purposes." This "game-purpose" is pretty much inarguably the oldest and best-demonstrated of the bunch, having been the heart of the first TTRPG. As a result it can sometimes be glossed over as being intuitive or already explored because it is old hat, but this is not always the case (as Clearstream has demonstrated purely by making this thread!)
Groundedness-and-Simulation. Though a popular interest, this "game-purpose" has occasionally struggled to see effective design, perhaps because it focuses least on any specific part of the phrase "roleplaying game," being neither about the role one plays, nor about being a game in the sense that S&A is. Rather, G&S is about the process of inserting or immersing the player, via their character, into the fictional world with its various rules and components, and letting things naturally advance, with minimal influence or modification by the person facilitating this experience once the ball starts rolling. In many ways, this is where TTRPGs intersect most with auteur cinema and authorship as in novels; there is a huge emphasis on worldbuilding and consistency and precision.
That's where "
Groundedness" is established: someone (almost always the GM or the author of the premade setting or adventure) setting up a believable, cognizable, "realistic" (but still fantastical) context. This is vitally important ground work for the process of play, as an ungrounded fictional context is too unreliable or too incoherent to make sense of (unless that sort of thing is the point, e.g. the context is a dreamworld or the like where inconsistency is expected, but that's a rare exception where minimum Groundedness has a grounded reason for being very low.) Then, players themselves advance the state of the world (with the GM/module/system doing the behind-the-scenes heavy lifting) via naturalistic, context-appropriate decision-making:
Simulation. They collectively Simulate (read: run the processes for an intended accurate model of) a world and its inhabitants and how they would process and respond to the established world and its rules.
Unexpected, emergent phenomena often result from these things. The intended gameplay loop usually involves having a goal within the established world (usually, but not necessarily, GM-provided) and a set of resources (possibly including information and time as "resources") which may be turned toward that goal, with the best play occurring when one finds a satisfactory path to that goal which employs those resources in clever or efficient ways or leverages unexpected confluences of the rules. Reasoning, extrapolation, and prediction are highly valued.
Conceit-and-Emulation. Almost as old as G&S (it's hard to tell which came first), but moving in very different directions, this is the "game-purpose" of faithful depiction of a theme, what is called a High Concept in cinema. Internal physical/naturalistic consistency is of minimal relevance, instead the High Concept is king, dictating what design elements will be included and wrapping the gameplay loop around itself. In general this High Concept, which I call the
Conceit, will be chosen by the GM herself, though it may come from an outside source, or might even be collaborated on by the group, but rarely if ever will arise from an individual ordinary player picking it. From there, the gameplay loop focuses on developing satisfying and (ideally) enlightening portrayals of the Conceit(s), which is "
Emulation."
Where an ultra-pure S&A game just cares about besting challenges and superlative success, and an ultra-pure S&G game follows naturalistic reasoning wherever it may lead, C&E welcomes elements that enforce the tropes or characteristics of the Conceit even if they might not be "effective" or "realistic," because the purpose of play is to elevate Conceit so that it can be appreciated more. Genres are one of the primary options for Conceit, but other choices are not unusual ("wacky hijinks" comedic games, for example). Because of this interest in Conceit, this "game-purpose" is much more amenable to active-in-play GM force than the previous two in their pure forms would be. (S&A generally opposes GM force outside of setting up the opposition/challenge, while G&S generally opposes GM force once the Simulation has started unless it is needed to expand the world content in a direction that hasn't previously been fleshed out.) Making "behind the scenes" tweaks to ensure a fulfilling portrayal is welcome here.
Values-and-Issues. The most recent, and most easily misunderstood, game-purpose. Here, the point of play is for the players themselves to declare what matters to them and then pursue or abandon those things specifically through the process of play. When this is actually facilitated by the system, it means the players have tools for establishing their
Values in a concrete way, usually with incentives or rewards for doing things that exemplify, test, question, or invalidate these Values. Where a Conceit is more like an
ambiance, a tone or vibe pervading the overall experience, Values are specific to each character and (typically) chosen by the player, since it can be challenging to
choose to care about something that someone else has imposed on you.
But if you merely said, "I care about X" or "my goal is Y," that wouldn't really get anywhere, would it? To actually go somewhere, there must be some form of conflict or difficulty (all the "game-purposes have some kind of conflict, they differ on where it's located and how it's processed). For V&I, conflict arises in the form of
Issues: points of uncertainty or even crisis, where the Values are on the line. An important characteristic of Issues compared to other conflicts, though, is that they generally
follow after the set Values, rather than being decided separately in advance (as is generally the case for most other "game-purposes.") In the crucible of Issues, Values are tried and the resolve and beliefs of the character are put to proof. As a result, particularly in comparison to S&A design, "success" is generally not
unequivocally preferable to failure even at the small scale--which is part of why "Fail Forward" is a technique strongly associated with games of this overall "game-purpose," such as Dungeon World. "Success" is nice, sure, but the "be a protagonist, face difficulty" gameplay loop functions little differently whether goals consistently succeed or consistently fail (though there's certainly a likelihood of darker characters if they fail all the time!)