Old North State vs North Carolina

Old North State and North Carolina both are nouns.

Word	Noun	Adjective	Verb	Adverb
Old North State	Yes	No	No	No
North Carolina	Yes	No	No	No

As nouns, Old North State and North Carolina are synonyms defined as:

Old North State and North Carolina: a state in southeastern United States; one of the original 13 colonies

Other synonyms of Old North State include N.C., NC, Tar Heel State.

Old North State (noun)	North Carolina (noun)
a state in southeastern United States; one of the original 13 colonies	a state in southeastern United States; one of the original 13 colonies
	one of the British colonies that formed the United States, with capital Bath, Edenton, Brunswick Town, or New Bern