do these two cars have the same turbo....ive heard the 1.8t has a t03 and the 337 has a k03 sport i was wondering if that is true?

all newer models with engine code awp have k03 sport turbo, awd have standard k03 turbo (note:2002-up all have awp engines)
what is the real difference with k03 and k03 sport?
k03 has k03 compressor and k03 inlet
k03 sport has k04 compressor with k03 inlet(basically this has k04 compressor with smaller inlet)