You'll have to excuse my ignorance, but I don't recall the later NFSs and I don't think I ever played early Ridge Racer. What bits did they copy? Gating through currency/licenses?
Need For Speed III was about the same as every other racing game on the market at the time (and was essentially identical to the first two NFS titles, albeit arcade like II rather than a sim like the original). You enter racing series and gain points, or enter race series where the last driver in each race is eliminated. If you have the most points at the end of the series, you automatically unlock the next level up cars. Same as Ridge Racer, same as Destruction Derby, same as Test Drive, same as Demolition Racer, same as Wipeout, same as Lego Racers, etc.
Need For Speed High Stakes was the first NFS game that released after GT1 (Hot Pursuit came out before GT1 released internationally), and it threw the entire career structure out in favor of an open ended credits based system offering car customization and a
much more realistic design ethos. The track design was toned down dramatically. The car physics were made much more tangible (albeit still very arcade). The car list was turned from the straight up supercar fest it had been in NFS II and III to a roughly 50:50 mix of regular cars and straight exotics.
Porsche Unleashed then took the GT car ownership concept even farther than GT did at the time. Hot Pursuit II marked a temporary reprieve back to the traditional arcade unlock system of the first 3 games; but after that they threw out the book and went right back to a credits based customization system (ultimately culminating in Pro Street, which took the GT design ethos to a T and slathered it in a thick coat of the whitest urban slang ever written).
Ridge Racer is a bit more complicated, because the game that most closely aped GT in terms of
structure (Rage Racer) was released
before GT1. After that Namco pulled way back from everything the game did until Ridge Racer 6 (mostly because Rage Racer, while really cool as an idea, wasn't very... good. Ridge Racer 7 was much better executed), when they reintroduced all of the credits system and car "tuning" stuff. But R4 was instead a direct stab at the "more more more" fever that GT1 started. Namco directly compared to two on the box art, and happily talked about the same things in advertisements for the game that Sony talked about GT1 about:
And absolutely filled the game with cars that weren't really things that existed, but were obvious enough in their lineage. Plus the fancy force feedback "steering wheel" controller that they put together specifically for the game. They're sights were damn higher than they had ever been before, though truthfully they were closer to a proto-TOCA Race Driver but with GT levels of content. Then compare that to Ridge Racer 64 and Ridge Racer V, which basically pared all the way back to generic arcade games.
Even the Destruction Derby series went from arcade enough that you expect to have to insert quarters to basically a carbon copy of the GT progression system; with car purchases, upgrades and car customization.