It's a bit more complicated than just K03, K04 etc. Borg warner/kkk's clasification system is pretty complicated, compressor wheels are identified by a 4 digit number. the first 2 are the exducer size in 10th's of an inch, the seccond 2 are the size of the inducer given in a percentage of the exducer, for example a 2275 wheel has a 2.2" exducer, 1.65" inducer (75% of 2.2) ! Heres a breif rundown of the differences between the turbos most people fit to their mk4's:
K03-K03s differences, K03 has a 2073 compressor wheel, K03s has a bigger/better 2075 wheel, exhaust side is exactly the same. (same turbine, same 22mm wastegate)
K04-001 - similar 2075 compressor wheel as the K03s, slightly larger turbine, larger wastegate, direct replacement for the K03/K03s
K04-02x - 2275 compressor wheel, larger turbine than the K04-001, will not fit a mk4 without buying a different exhaust manifold, downpipe, tip etc.
There are literally hundreds of different variations of K series turbo's.
Hybrids, here's a pretty damn epic thread by dan aka littco aka beachbuggy.
http://www.audi-sport.net/vb/a3-s3-forum-8l-chassis/139858-hybrid-turbocharger-k04-build-3.html