Car numbers used to be assigned by branches. They are now transitioning away from the car numbers and the newer vehicles are being stripped only. The license plate is generic to the State and the vertical numbers will let you know which year the vehicle was made and the horizontal numbers are randomly assigned.
Regarding the call signs, those do go by branches. Executive are 100's, Technical Rescue are 200's, Fire Operations and Training are 300's, Fire & Life Safety are 400's, Operation Support are 500's, Fire & Arson Investigators are 600's and Hazmat are 700's. If you hear a number from 0 to 20 that is most likely a boss, for example 200, 300, 400, 500, 600, 700 are Branch Chiefs and then the rest would be Deputy Chiefs.