Not sure if you have the wrong end of the stick here or what. But Notts with an S is basically reserved for Notts County. When referring to Forest it's either just Forest or Nottingham Forest. This has nothing to do with abbreviating the name of the club. So it is not the same as Brighton and Hove Albion being called Brighton or Albion or whatever else. It's not the same thing.
Now i understand , i genuinely never knew that , thanks you live and learn .