Does NYS of the Feds have a definition of full-time or part-time employment??

No state or federal law defines what constitutes part-time or full-time employment. It is whatever the employer says it is. 40 hours per week is often used, but that's probably because that is the threshold of hours worked before overtime is due for nonexempt employees. It could be 35 hours, 32 hours, or even 45 hours (theoretically). In any case, this is not an area regulated by law.