While both are made by the MINI they are different. The Cooper is a coupe or convertible. The Countryman is a small Sports Activity Vehicle that is larger than the Cooper in every way. All are...
The Cooper and Cooper S have different exhaust outlets. It is not possible to use an S exhaust on a Cooper without modification to the spare tire carrier (if the car has one) and the rear bumper.
the 2002-2006 model has a supercharger that's what the 's' stands forthe 2006-present has a turbocharger but it is still called the 's' as it is heritage for the fastest mini to be called the mini...