The ethos of the Gen 1 Type-S was "winding road spec". This is directly from Honda marketing at the time. The S was a NSX that was designed less for the urban professional and more for the owner who wanted to head out on the weekends and enjoy the back roads. It preserved all of the luxury amenities that customers expected from the NSX, but firmed up the ride an deleted weight to make the car feel better on those winding roads. The R was always sold as a "track day" NSX. Honda tried to force the point by making the radio and A/C optional at a fairly large cost. Thus, the R and S specs, while both performance-related, are aimed at completely different customers- at least in Japan.
Setting that aside, the R and S are also brands and there is some kind of rule or understanding that R belongs to Honda and S belongs to Acura. Looking at the Type-S trims for the Acura lineup, it does appear to fit the original Honda ethos for the S: performance luxury. These aren't stripped out track cars- they are luxurious Acuras with a little extra performance. Acura has never really sold a track-ready trim level- except for the Integra, which, incidentally, was sold as a R. I think both the TLX and NSX could carry a track-spec trim level, but for some reason Acura does not want to step into that space. It's odd, considering they are casting themselves as a "performance" brand.