Actually, none of the above...NC was known for its naval stores..or exports of sap (tar) from pine trees for sealing the seams on boats before the Civil War...
During one of the battles (I don't remember which one) ..the NC troops stood their ground instead of retreating like some other units...the Confederate General in charge made a comment after the battle that he wished he had more troops like those from NC..."They held their positon like they had tar on their heels"...The name "stuck"....LOL