The Carolina slaw dog is decided by the slaw, which is the one topping doing the work the others cannot. A frankfurter goes into a soft bun under a thin local chili, a stripe of yellow mustard, and chopped onion, and then a mound of coleslaw goes on top as the finishing layer. Across the Carolinas this is the default order, not a variant: ask for a hot dog "all the way" and the slaw is assumed. What defines the build is that the slaw is structural, not a garnish. It is the cold, crunchy, acidic cap that keeps a warm, soft, fatty dog from reading as one heavy note, and the rest of the assembly is arranged so that cap stays on and stays crisp.
The craft is in the chili and the order of operations. The Carolina dog chili is thin and fine-ground on purpose, closer to a loose sauce than a stew, so it clings to the frankfurter along its length and soaks lightly into the bun instead of falling out the ends in clumps. It goes on first, against the dog, with the mustard and onion, because those are the wet, warm layers. The slaw goes on last and on top, never folded in, so its shredded cabbage stays crunchy and its dressing's acid sits where it can cut the fat of the chili rather than dissolving into it. The slaw itself is the regional tell: a fine-cut cabbage slaw bound just enough to hold, sometimes plain and tangy, sometimes carrying a little of the same tomato-and-vinegar note as the local barbecue sauce. The bun is kept soft so it yields against the load, and the whole thing is built fast at a counter and handed across before the slaw's moisture works into the bread.
The variations are mostly which layers a given stand assumes by default. "All the way" is the full build above; dropping the chili leaves a slaw dog in the plainest sense; some counties run the slaw sweeter and some sharper, tracking the local barbecue palate. The pulled pork and whole hog sandwiches carry the same regional flavors onto a bun instead of around a frankfurter. Each of those is a codified build with its own logic and deserves its own article rather than being crowded in here.