Does wait() depend on the player's FPS at all?

I was wondering if wait() would have any delay if the user’s FPS was lower than 60 FPS. Like if I did wait(1) would it still wait the same amount of time on a user that has 60 FPS and another that has 30 FPS?

Yes, wait does depend on the clients performance.

What if the wait was inside of a server script?

then it would depend on the server and not the client. It would only lag if the server itself is laggy.