As others have stated, it varies by state. I've heard that some states require the permit holder to state, on the application, what they will be carrying and then restrict them to that. Some states require that the weapon be concealed at all times (I think I read that Ohio requires concealed carry, but then requires open carry while in a vehicle). The ability to conceal places some practical restrictions on what can be carried (unless you want to get creative).
TN simply states that the permit is to carry handguns (any handgun or any number) and doesn't bother with the word "concealed". Concealed is advised, though, to avoid extra attention from the more enthusiastic police officers or excess cell phone calls to the police. I've heard of one incident at a gas station where a woman flipped out and started screaming for someone to call the cops, because a permit holder stepped out of his pickup and started pumping gas while carrying a handgun in a normal belt holster. I wonder how she would have reacted if he had been carrying an AR pistol in a tactical holster (pictures of one, made for an M4, have been posted in the AR pistol forum, but it is apparently out of production)?