Are road numbers like serial numbers, meaning are they unique to that particular RR company. Also, when models are made for railroading, are the road numbers real or do they just put any old number on the scale models?
Each railroad numbers its freight cars as it wishes. The initials identify which railroad (or private car owner) the car belongs to, and the number is unique to the car. On one railroad 123456 may be a boxcar, on another it might be a gondola. There have even been a few very rare instances documented where a painter messed up and there were two of the same number on the same railroad. That was back in the pencil and paper days, with computerization something like that would be found out pronto today.
For the most part I think models these days are accurately numbered although I am not into modeling. Years ago some manufacturers did, and some did not, use correct numbers. When Tyco first made GP20 models in the 1960s, every one, of every different railroad offered, was numbered 5628 (which I think was the number of the demonstrator, but I'm not sure)