[Both posts are semi-correct. When Princeton University was founded it was called "College of New Jersey", which is why The College of New Jersey had to abandon its initial use of the initials CNJ, and instead go to TCNJ, which it steadfastly sticks to. When the name was changed, the incorrect signage said "The College of New Jeresy" not "The College of New Jesrey". Rutgers University is the "official" university of the state of NJ, though TCNJ and others are also partially funded (and have some minimal oversight) from the NJ government.
The College of New Jersey was founded in 1855 as the Trenton Normal School, which didn't mean it wasn't a weird place; it meant that it was a preparatory school for teachers.