Factory JCW or Cooper S with Body Kit?

[roygarth]

The car is a 2007 and the elderly owners says, and I think believes, it is a factory JCW.

But if you put its reg into Autotrader it says Cooper S. I tried another 2007 JCW and it says JCW.

What should it say on the V5?

How else can one tell?

Can BMW tell from the Reg or VIN number?

Thanks!