North Carolina vs Tar Heel State

North Carolina and Tar Heel State both are nouns.

Word	Noun	Adjective	Verb	Adverb
North Carolina	Yes	No	No	No
Tar Heel State	Yes	No	No	No

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

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

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

North Carolina (noun)	Tar Heel 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