The Mfg'rs model nomenclature can drive one nuts...here are some links
to make your hair hurt, in terms of discerning the real "differances":

FZ6R 2009 Yamaha FZ6R
YZFR-6 2009 Yamaha YZF-R6
FZ6 2009 Yamaha FZ6

And, the FullTiltBoogie R6S version:
2009 Yamaha YZF-R6S

Any of the above are seriously fast, amazing handling 600 cc class m'cycles, if
used in capable hands.

For a first street sled, I would look for used, 600 cc max, (less would be ok, imo,
based on your size & lack of riding experience), etc. And, used could be a couple,
three, four years old.
There are garages full of sleds that don't get ridden much after the first year or
so...though, used m'cycles require as much investigation, or more, than used
cars.