Bomber Harris... Things have probably changed, but when I was working what we saw on the screen had nothing to do with what you input to the FMS apart from your transponder code. That code - as issued by ATC - was paired with the callsign from your FPLN by some sort of computery to provide a label on the radar display. So at the position of the a/c we had the callsign, altitude/FL from your Mode C and one or two other items for our use provided from the radar equipment. I understood that Mode S transmitted a unique code which could also be paired with information from a ground database to provide registration information. Hopefully someone better qualified can help here?
The SBS device in question is quite clever. Using a very simple antenna - something a WiFi antenna, it can display on a PC a picture similar to a radar display. Aircraft using Mode S are displayed in their correct positions using information transmitted from the a/c. To those who have never seen a radar it's a piece of real magic, but to those who have.... well......