You are correct. There is a general "tire" model and each group is just a modified amount of lateral and longitudinal grip. This has always been the case. The underlying model might change, but the philosophy has always been the same.
Lots to unpack here.
I've been to the same track, two weekend in a row, and be over 1 second a lap different in timing. That's the same person, same vehicle, same set up, same track, just different days. The point being, there are lots of little things that can affect a lap time.
The only truly valid comparison is if a person were to drive a car in real life, at a given track, and then go replicate that as best they can in the game. So, for instance, fly to Japan and lap Tsukuba for real. Still, as mentioned, the tires are a big differentiator, never mind that the underlying system of the game is the same basic car system with modifiers for everything else. So, IMHO, comparisons to real life are difficult to make at the best of times.
Not to mention the lateral forces on your body. That alone will change the performance over a lap.
Again, this goes back to the reality of the game being 1 basic tire, 1 basic car, and modifiers for everything else. As the game evolves and they chase a better "model" the values change as well. The amount of adjustment now maybe be radically different to the previous titles. You can't really compare it. You can compare the "feel" but everything else is kind of incomparable.
I think that, given that Michelin is a featured provider of the game, it's reasonable to make comparisons with their line up of tires. I had Michelin Pilot Super Sports on my golf. 235/35/19's. I would consider this to be an SM tire (because there are longer lasting, harder sport tires available). The Pilot Sport Cup 2 R is a track tire, but not a slick, so I would consider that an SS tire. What tire would Michelin have as a CH, or CM, or CS? What's their performance difference?
This is just my opinion though.
Here's the link to Michelin's page of tires. You can somewhat see where these would slot in to the game, but again, this is just a supposition. I have no idea if they even thought about trying to simulate these tires in any way.
https://www.michelin.ca/en/auto/browse-tires/all-tires