For this disucussion, Joe is flat average stats for a human. He is competent in whatever it is you're trying, but not to elite nor professional (IE, Master's Level or equivalent) levels.
For Level based games, usually assume level 1.
Exemplars for Illustrative Purposes
I refer to the following, so the precis is presented so you can follow the actual answer portion without doing research...
In MegaTraveller, the task system is based upon a roll of 7+ on 2d6 being "Routine" for a person with Skill 1 and +1 from attribute. MT also defines skill 1 as employable, and Skill 3 professional (as in, doctoral or masters degree trained fields should result in skill 3).
which means it's a mishap on a 2-3 (3/36 chance), fail on a 4 (also 3/36), leaving 5 a marginal (4/36), 6 (5/36) moderate, and 7+ (21/36) exceptional success.
MT also defines Impossible as 19+... given that there's effectively a DM+4 for taking extra time (but it's expressed as a difficulty shift), and given the DM+1 from stat, and DM+1 from skill, Joe Normal simply can not perform an impossible task. His max roll of 12, +4 for extra time, +1 for stat, +1 for skill is a mere 16. Even with peak stat, for DM+3 instead of +1, without a skill better than 1, Impossible remains just that: you can't get there.
A natural 2 is always a failure.
The overall scale, and Joe Normal success rates (Adj TN, chance of Adj TN, and % chance):
Simple 3+ (3+ 35/36 97.3%)
Routine 7+ (5+ 30/36 83.3%, ExTime 3+ 35/36 97.3%)
Difficult 11+ (9+ 10/36 27.7%, ExTime 5+ 30/36 83%)
Formidable 15+ (13+ 0/36 0%, ExTime 9+ 10/36 27.7%)
Impossible 19+ (17+ 0/36 0%, ExTime 13+ 0/36 0%)
The labels and processes are the same, but the definitions of Joe normal differ. Joe has a DM+2 from attribute, DM+1 from skill, and the die-roll is 1d10, not 2d6... so the odds look like:
Simple 3+ (2+ 90%) note minimum failure of 10%
Routine 7+ (4+ 70%, ExTime 2+ 90%)
Difficult 11+ (8+ 30%, ExTime 4+ 70%)
Formidable 15+ (12+ 0%, ExTime 8+ 20%)
Impossible 19+ (16+ 0%, ExTime 12+ 0%)
Twilight 2000 2E, Dark Consipiracy, and TNE
1d20 for Stat+skill or less for a difficult task. Average stat is 6, baseline skill is 1. Same labels, extra time rules, and many other similarities with MT and 2300AD... including publisher and design staff. Each level is a double or half, extra time is a full level.
For Joe Normal:
Simple x4 (19- 95%)
Routine x2 (14- 70%)
Difficult x1 (7- 50%)
Formidable x1/2 (3- 15%)
Impossible x1/4 (1- 5%)
WFRP 2E, Dark Heresy, Rogue Trader, and Deathwatch
The default task level, called challenging, for a skilled charcter is a percentile equal to attribute; this means an default level roll is roughly 31%, tho' the overall range is 17% to 70% for humans... But Routine is defined as +20 to the percentage. Trivial is +60, Difficult is -10, and Hellish is -60. Which means a hellish task is bloody hard for even the best characters, with 70% stat, +20 from skill, and +10 from a relevant trait; with +10 from help, peak chance is 50% for maxed out experience uberman.
D20 and 3.X D&D
I'm not positive I've got the labels right, but given the DCs, Joe Normal, level 1, with a +4 total bonus:
Automatic: DC5 (100% or take 10 for 100%)
Easy: DC10 (75% or take 10 for 100%)
Moderate: DC15 (50%)
Difficult: DC20 (25%)
Very Difficult: DC30 (0%)
Note that the take 10 mechanic means that Easy tasks are done automatically if skilled in them.
New World of Darkness
In World of Darkness, an average person is defined as having two "dots" in each attribute, and cursory training in a skill is one dot. Three dots gives the character three ten-sided dice. If any die comes up 8, 9, or 10, that's success, so the chance of failure is (7/10)^3, and the chance of success is 66%.
Difficult tasks may require more than one success. Each roll that comes up "10" earns another roll, so with luck a dice pool of three can attain four or more successes:
- Two or more successes: 26%
- Three or more: 6.7%
- Four or more: 1.3%
- Five or more: 0.2%
Savage Worlds uses a single die roll of a size determined by your skill level; a character of basic competence will have a d6. Roll the "target number" or higher to succeed. The default target number is four, so that's a 50-50 chance: 1, 2, 3 is failure; 4, 5, or 6 is success.
However, "wild cards," meaning PCs and important NPCs, get to roll a "wild die" too, and take the higher result. This wild die is always a d6. The higher of 2d6 against the a target number of 4 gives a 75% chance of success: failure requires both the skill die to come up 1, 2, or 3 and the wild die to do the same. Each of these has a 50% chance to happen, so the probability of both occurring is 25%.
Difficult tasks will have a higher target number, but both die rolls are "open-ended," meaning that rolling the highest possible result (6, in this case), known as an "ace," lets you roll again and add the new result, repeating as long as you keep acing.
- d6+wild die vs TN6: 30.6%
- d6+wild die vs TN8: 25.8%
- d6+wild die vs TN10: 16.0%
Burning Wheel doesn't really define "average," but a skill of B3 is common for a junior non-specialist. As with World of Darkness, high rolls count as successes, and the difficulty of a test, known as "obstacle" is defined by the number of successes required. Burning Wheel is more generous in that it uses d6s, and a 4, 5, or 6 counts as success for normal character, so each die is basically a coin flip.
- B3 vs Ob1: 87.5%
- B3 vs Ob2: 50.0%
- B3 vs Ob3: 12.5%
Generally, most systems take a baseline skill level (and if relevant, attribute level), and define task labels relative to this. They don't really give hard and fast ideas, but generally put the chances of success for a trained character at a routine task about 50-75%.
All the other breakpoints vary widely, but in general, most will have a set minimum success chance, and most also have a maximum success chance.
A few games instead label difficulties by how good you have to be to have a given chance.
The label order isn't even terribly consistent, other than the basic 5: Automatic, simple, easy, moderate, difficult. Exactly what those mean, however, varies too widely to generalize.
It truly means, no matter what system, you need to work out the percentages yourself, and you need to figure out what a particular difficulty label truly means. It also helps to figure out what the defined baseline is for those labels.
Note the extra time listings for MegaTraveller; when not rushed, a competent character can take extra time and make routine tasks fail only 2.7% of the time; even semi-skilled characters (skill level 0 but not unskilled) doing so is still that 97.3% chance of success.
Note the similar break points despite the different die-roll for 2300AD and MT... same company, similar meanings. Actually, the task system for MT was invented for use with the prior Traveller edition, by a 3rd party (Digest Group); It was then adopted and adapted for 2300AD, THEN reverted back for MegaTraveller, since MT was essentially collated by Digest Group. T2K2.2 and Dark Conspiracy have similar breakpoints... but much wider difference between peak characters and poor.
It's all just guidelines. Shortcuts to get you up to a better level of GMing competence faster, by giving you labels. But those labels have to mesh well with the skill levels listed, too. When they don't, when the odds are too out there for players, they often reject the whole system because the labels don't meet their expectations. With MT, I've lost a few players because they thought Routine was too hard as written, and no level should be labeled "Impossible"...
The Usual Approach
The usual approach is this: The labels usually work for the "Normal Guy" with "A reasonable level of skill" doing a "Normal task"...
You just need to approach all task labels from the idea of "How hard would Joe Normal find the action" and then pick the difficulty.
As a designer, the folks at GDW followed this same approach.
The Alternate Approach
A few games define difficulties by skill level at which success is expected. Fudge, as well as Fate and other such derivatives of Fudge, defines skill levels and difficulties with the same "ladder" of skill. Just define what skill level you would expect to succeed 60% of the time, pick it, and there's the difficulty.
The exposition of GNS theory itself denies that a "pure" game of any of those is possible while still being a roleplaying game, but we can easily talk about simulation-heavy games, even if we can't talk about "pure" Simulationist games.
From the gist of this question as I understand it, you're just puzzled that you can find strong examples of only Gamist and Narrativist games, and you only really need one example to be satisfied that exemplars of heavy Simulationism exist generally.
For the one counter-example I would offer HârnMaster in any of its editions. Concerned with simulating a medieval-like world, it dispenses significantly with balance among characters or "encounters", and its mechanics are not built to emulate a narrative structure, leaving it low on Gamist and Narrativist scales and high on the Simulationist scale.
Simulationist games are rare in practice because it takes quite a strong commitment and taste for simulation to enjoy a game that tries so much to not be very game-y. It takes significant intestinal fortitude, so to speak, to put up with a first play session that entirely involves being a hapless serf wandering alone in the forest after fleeing your lord's lands and then dying to blood loss from a wolf tearing open your leg, and to put up with it enough to actually enjoy the immersion of that hardcore degree of simulation. Such gamers exist (hi!), but those who can enjoy Simulation to the near exclusion of Gamist and Narrative controls on events are few enough that they're not often catered to.
Besides, doing Simulationism well is the first "tech level," if you will, in the development of RPG design history, so such gamers are already well-served by existing games. So that's another reason you're having a hard time finding them: the majority if them are old games, with few improvements left to make that their audience would care for.
Rob Conley has written an extensive Actual Play post on a session of HârnMaster that is a good example of what a Simulationist game ends up being like. There is a lot randomly generating character details in order to create a character that has a background and starting features that are statistically realistic in the setting (such as having an allergy to shellfish, being born of low stock, having been enslaved, or lamed at a young age). Play involves a lot of "slice of life" detail that makes the world feel like a real place. Of particular note on the Simulationism/Gamism difference, note the nature of the cave in that play report: no smooth floors and interconnected passages on a consistent level as a way of making caves convenient for gameplay reasons – instead, it's like a real cave, with frustratingly fractured terrain that barely qualifies as a floor, difficult squeezes, and the rare flat area that's inhabitable. Note the way combat works, too: it's all about injuries, shock, passing out from pain, playing to your strengths when you can, and suffering the turns of random luck when you're not playing to your advantages. There is heroism there; but it's small, hard-won and not taken for granted, much like a hero you'd read about on the local news is a hero for having good luck at the right time and place when they could have as easily ended up a victim.
A final note.
This answer starts by taking GNS theory as a given and works inside that framework to help explain it. In reality, GNS has a lot of holes and problems – enough so that it's largely considered flawed and obsolete, even by its creator Ron Edwards. However, its replacement, the Big Model, is a many-tentacled beast that is hard to get a mental grip on, and it still uses the fundamental concept of a threefold division in major play styles (and so doesn't thoroughly repudiate the GNS way of thinking about roleplaying), so in practice it hasn't supplanted GNS theory in the popular discourse. The Big Model does attempt to address the discrepancies that people are pointing out in how GNS gets (mis)used, though – the quibbles with me calling a game "Simulationist" are entirely fair. Still, it will be some years or decades before we can expect talk of "Simulationist games" to fade away and be replaced by talk of designers who mechanically support a "right to dream" play agenda.