R56 Cooper or One - how to tell??

[1750jb]

I was looking at a 2012 R56 which was advertised as a One, but it had a Cooper badge on the boot (obvs an easy thing to fit) but it seemed pretty sharp to drive, and I wondered what exactly the differences are. Are there any trim or under bonnet differences between the two that would be there to be seen?
Also is the power difference a remap or are there mechanical differences between the 98 and 122bhp engines??

Thanks /

[1750jb]

Perfect guys / cheers