North Carolina vs Old North State

North Carolina and Old North State both are nouns.

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

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

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

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

North Carolina (noun)	Old North State (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