Well my knowledge on the MINI's are limited but from what i've seen there are both engine & body differences, the black cooper S has a 1.6 ltr supercharged engine with a small top mount intercooler and a dual exhaust. Also it has a 6 forward gearbox. I think the power output is 160bhp or 165bhp.
Body differences are mainly the hood scoop for the intercooler, the dash has a brush aluminum look to it, front bumper has a bigger air intake, less chrome, and 17 rims are standard.