Digital noise comes from a lack of photons. All that setting an ISO of 800 does is to change the way your camera calculates exposure in whatever auto mode you’re in, then pushes the overall gamma.

That said, digital noise is spectacularly unlike grain. IMO if you are shooting digital and want film grain, get the cleanest shot you can, and add it in post.

Disclaimer: when I was shooting film it was almost exclusively Velvia/Provia, which says a lot about my preferences on grain.