When I was developing parts of the curriculum for the University of Advancing Technology's Serious Games coursework, there were very few source materials to draw from; ten years on, there still seem to be very few standardized critical frameworks for discussing and analyzing the many different styles and types of play lumped together under the "serious games" label. The following is by no means an attempt to be definitive or establish a standard, but rather to spend some time thinking aloud about the boxes we use to compartmentalize our projects and how we might sort game design approaches more accurately for examination.
I began my material for these courses by identifying five different approaches to simulation, in the context of "serious games" (I continue to use the quotes, not as sarcasm, but as an indication of how dubious I am about what this particular label can tell you about the product itself). These approaches bleed over into games for entertainment, which is a natural occurrence as both, at their core, promise some degree of interaction (and yes, fun.) These approaches are on a gradient, so to speak, from the most sincere and direct attempts at simulation to approaches that try to balance simulation with the abstracted world we associate with video games.
Those games/interactive products which most directly attempt to mirror or mimic reality, I classified as Mimetic. This means "mirror image"; these sims attempt to create the most realistic and authentic experience and may have little actual "game" content.
Mimetic sims do not rely upon visual fidelity to create a sense of simulation; instead they attempt to engage the imagination of the player or user and do not sacrifice realism for attractive graphics or traditional gameplay elements (such as earning a score). The goal is to re-create an authentic experience, for someone who has experienced this before to some degree in the real world.
These sims are made for a small, "hardcore" audience and may include such non-game subject matter as air traffic control, orienteering, mountaineering, traffic management, stock market trading, and hydrology. Often there is a high emphasis on educational content and an assumption that the player is very familiar with the source material, if not in fact already a professional in that field. The core approach of a mimetic simulation is to duplicate the interaction points between the human and the system being simulated with 1:1 fidelity; so a mimetic air traffic control simulation would be real-time and include all the associated duties, perhaps even as far as not including the ability to pause the game (as, alas, we can not pause time in real life).
Though they are produced for niche audiences, mimetic sims are in fact much more common than you would think, especially in the areas of training simulation. On very rare occasion (fueled by massive contracting budgets) you would find a commercial simulator that also attempts 1:1 visual fidelity, but again this is for presentation of information and not aesthetic purposes. One example of this would be a commercial flight simulator - these feature extreme visual fidelity for weather, time of day, lights on the ground, etc. but do not actually simulate the crash of a plane if the sim pilot is careless; on Mythbusters, when they crashed the plane in a full-cockpit simulator, it just skidded and bounced off the ground. Thus the goal of visual mimetic presentation stopped at the point the simulation stopped, rather than continuing into a more game-like presentation of a spectacular crash.
A few examples: http://www.catchingfeatures.com/ is an orienteering simulation; http://www.atc-sim.com/ is a control-tower simulator; https://www.circuitlab.com/ simulates working with digital circuits.