Old news, there is definitely a difference between "University of New York" and "New York University". If you take a gander across states, you'll likely find that there are often dual university systems. University of Missouri vs Missouri State University... University of Illinois vs Illinois State University. There is a difference between New York Attorney General and Attorney General of the State of New York. There is a difference between Emperor of Germany and the German Emperor (was regarded by Otto von Bismark to be superior than the former). The difference between "New York" and State of New York is that New York refers to a nation. The State of New York seems to refer to a trust, an estate (i.e. state) or other type of organization. However, in statute "New York" might be defined to mean or to be short for "State of New York" or for "the State of New York".
It might be worth noting or researching whether or not New York ratified the Constitution for the United States of America.