I feel like it conveys a totally different tone, and therefor has a different function in communicating

You're forking right it does.

Censored f--k or f*ck or whatever doesn't really convey a different tone, other than trying to say something without saying it. Which is annoying and frustrating, it puts work onto the listener that should have been done by the communicator.

Fork does come out with a different tone, because it doesn't sound as harsh. It's like how saying shit is a bit less severe than saying fuck - fork would be less than both of these, maybe on par with crap.