Carolina, in this case, refers to the name of the institution. This is likely based on its history. UNC-Chapel Hill used to be the only public institution of higher education in the southeastern US. Over time, UNC evolved to become the name of the system of schools that includes UNC-CH, NCSU, and 15 other campuses.

To this day, however, UNC-CH is still often referred to as Carolina, UNC, Chapel Hill, or - for athletics - the Tar Heels.