No, they refer to it as being on THE island, which cracks me up since Manhattan and of course Staten island are also islands. I’ll let you know the only reason I’m still at this is I’ve become fascinated how so many people have become so resistant to saying, ‘oh, right...’ on the internet.
Frankly, I’m originally from a village on the island, who thought it was so odd that people from my village called The Village in The City, “The Village.” To me, Long Island included only Nassau and Suffolk, which is why it’s so funny to hear Manhattanites refer to Queens as The Island.
Various islands of NYC
Brooklyn & Queens: The Island (which happens to be Long Island, but isn’t Long Island)
Nassau & Suffolk: Long Island
Manhattan: Da City
Staten Island: New Jersey.
(Joking about that last one.)
We went from Brooklyn to Queens then to Bay Shore, LI - I’ve never heard that Queens was ‘on the island’ - Nassau and Suffolk, yeah, but never Queens. Again, we escaped from NY when I was seven so maybe the designation was changed. :)