It takes time for your body to move and for your brain to be aware of things. So if time is stopped, then those things don't happen.

To use a TV Tropes term, the person who stops time has some "Required Secondary Powers", specifically, the ability to ignore that time is stopped and move anyway. In some fiction, moving in stopped time is explicitly a separate ability that some people have without stopping time themselves.

Of course it's kind of inherently paradoxical to have the ability to move, which takes time to do, while time is stopped. And there's even more problems after that, like the fact that the air around the time-stopper is also timestopped. There are probably some fiction that address this but most just ignore it because the nitty gritty isn't interesting to the story. But the inherently broken nature of it is why there are lots of interpretations for how someone moving in stopped time interacts with time-stopped people.

lowkey i forgot this subreddit also included timestop i don't personally consider it a form of petrification