There have been two Federation starships known to bear the name USS Carolina.
USS Carolina (23rd century)
The first starship Carolina was in service in the 23rd century. It was deployed to the sector near Capella IV in 2267, and apparently sent a distress signal to the USS Enterprise. However, the Enterprise had previously been diverted by a fake distress call from the SS Deirdre, and acting captain Montgomery Scott observed, "Fool me once, shame on you. Fool me twice, shame on me." (TOS: "Friday's Child")
- According to the Star Trek Encyclopedia, the Carolina was an old Daedalus-class starship with the registry number NCC-235. However, TNG: "Power Play" clearly states that all Daedalus-class ships were decommissioned by 2196, 71 years before "Friday's Child." Uhura spoke of the Carolina as a starship that appeared to be currently registered in the sector, not as an old, decommissioned vessel. Therefore, it's probable that the Carolina's status as a Daedalus-class ship is incorrect.
- The Encyclopedia contradicts itself concerning the registry number as well, listing it as NCC-235 on page 66 of the second and third editions, while page 417 (the starship list) gives a registry of NCC-160.
USS Carolina (24th century)
The second starship Carolina was in service in the 24th century. It was commanded by Captain Peterson. In 2377, it was deployed to intercept a Ferengi Marauder that was interfering with Project Pathfinder's communications with the USS Voyager. (VOY: "Inside Man")
Could possibly be a Nova-class starship as the USS Carolina is said to only have a max warp factor of 8