Here is a very basic list of what Level A, B, C and D means in terms of simulator capability in Europe. FAA is generally similar:
Level A
Complete enclosed flightdeck, all flight crew stations, all systems simulated.
Flight controls force v position tests with tolerances.
Basic motion and visual (night/dusk, limited field of view).
Objective flight tests, some with no tolerance other than "correct trend and magnitude".
Transport delay less then 300 milliseconds.
Level B (all training and checking, except takeoffs and landings)
As Level A, plus
Objective tests all have tolerances applied.
Level C ("zero flight time" for pilots with 1500+ hours in similar class of aircraft)
As Level B, plus
6 axis motion
180 by 40 degree continuous field of view, daylight capable visual.
Transport delay less than 150 milliseconds.
Extra objective tests for contaminated runways, controls dynamics, windshear, motion, etc.
Level D (zero flight time)
As Level C plus
Weather Radar simulated and co-ordinated with visual, TCAS, etc.
Objective sound and vibration tests.
Zero flight time includes base checks, but not the line check.
Some older sims will have "grandfathered" approvals based on the rules used at the time they were first approved. These have a G suffix, e.g. Level CG, but usually same training credits as normal Level.
Level D is an extremely high standard to achieve. By no means all full flight sims are Level C or D.
The age of the original aircraft can affect sim qualification, because if sufficient validation flight test data does not exist then a "special category" approval, based on subjective evaluation, is all you can get. That will be in the form of a letter from the CAA saying what training and checking can be performed. A Trident 3 sim for example could not even be a Level A device under current rules, and there's no chance of anyone flight testing one to get the necessary data now
As for MSFS not being a simulation, that's not true, but it is mostly about the eye candy. The MSFS aero model works in just the same way as in a Level D sim, only the data has much less resolution, less complexity, fewer coefficients and is not validated by anybody. The MSFS flight model is very simplified, so no one should expect to learn much about aircraft handling from it. What you can learn is radio navigation, procedures (though not on the included default aircraft), etc.