The FZ6 is based around the fuel-injected R6 engine and replaced the old carburetted Fazers which used the Thundercat engine when the emissions rules changed in 2003. The FZ6-S was produced from 2004 to 2007 when it was replaced by the S2 which has had a few minor tweaks eg better fuelling and less snatchy throttle coming out of bends and slightly better brakes, but there's not that much difference between them and AFAIK the S2 doesn't have noticably more power.Generally the easiest way (apart from production date) to tell them apart is to look at the instrument cluster, this is the FZ6-S and this is the S2.
04 - 06 FZ600 has Silver engine, silver frame, single circular speedo/rev counter, rectangular swinging arm and 2 piston sliding front calipers06 - ? FZ600 S2 has Back Engine, Black Frame, oblong Speedo with attached circluar Rev counter, 4 piston front calipers and chamfered edges on the swinging arm
04 - 06 FZ600 has Silver engine, silver frame, single circular speedo/rev counter, rectangular swinging arm and 2 piston sliding front calipers
I guess going by reg prefix will never be entirely accurate due to dealers sometimes selling off older non pre-registered stock..