Who comes up with these names?
Once upon a time the Transit Police was a department of the Transit Authority, employed by the TA and patroling the TA. All by it self, it was something like the fourth largest police force in the country or something like that.
Yet it was looked down upon by the NYPD and cooperation was sketchy.
Later (probably due to budgetary considerations) the Transit Police was made a part of the NYPD (no longer a factor in the TA budget) but a unit of the NYPD specialized in the transit system.
(And was not the Housing Police brought into the NYPD at the same time?)
MTA Police are separate, just like PATH police, their jusrisdiction extends across city, county and even state lines.
Elias