Yes, the NYState and Federal census were two entirely different enumerations.
You might check the web site of the NYState Library at Albany for a discussion
of these records (http://www.nysl.nysed.gov/gengen.htm  or the Archives:
http://www.sara.nysed.gov/)
  I'm unsure of the months of each (I personally haven't researched the NYS
census any earlier than the 1800s).  Not all counties are extant.  I do have a
printed list from the NYS Library giving the counties available in each census
year.
Best of luck,
Barbara