The Sega Saturn does not use the NV1, the hardware inside the console predates that chip by quite some time. But, they both make use of quadratic texture mapping.
The NV1 came out a bit early in the 3D acceleration era, around late 1995 and there was not a lot of competition at the time and no Direct3D, so there was lot of experimentation going on. SEGA was looking into porting some of their arcade and Saturn games over to the PC and they figured they might as well support that NV1 chip, since it was probably a little easier to port things over and also because CPUs were still quite slow. Also, they were in pretty good terms with Nvidia, but more on that later. The Nvidia NV1 probably found its way mostly in Pentium 90, 100 and 133 machines, so you can imagine just how slow some of the games ported would run using software rendering on these CPUs.
The NV1 didn't catch on, Direct3D became a thing and did not support the way that card worked, so everyone kind of moved on. SEGA ended up releasing a lot of Direct3D patches for their games and sometimes even newer versions all together. All things considered, I think most of their ports at the time are pretty lousy, especially Daytona USA, Sega Rally and Sega Touring Car Championship. Sega Rally 2 is a shining example, it's pretty much arcade perfect.
Interestingly, as I said earlier, SEGA was in very good terms with Nvidia at the time (1993-1995) which was a brand new company back then. In recent years it has been revealed that they were collaborating on a few projects, one of which was a hardware prototype that was supposed to be released instead of the Saturn, featuring the Nvidia NV2 chip and using cartridges as storage, as direct competition to the Nintendo 64 (then Ultra 64). Negotiations fell through, because this was being worked in the US and Japan was the division that made most of the important decisions. They still worked together with the NV1 ports on Windows, but when that chip failed, Nvidia scrapped the NV2 and moved on to the NV3 which was named the Riva128. And the rest is history as they say grinning face...