The defining thing about Alabama smoked chicken is that the sauce is white and the sauce is the point. Most American barbecue argues about red sauces, tomato or vinegar, applied to pork or beef; this is a whole smoked chicken finished in a mayonnaise-based sauce sharpened with cider vinegar, coarse black pepper, and cayenne. The chicken is dunked in that pale, tangy emulsion straight out of the smoker so it coats the skin and runs into the meat. On a bun, pulled or sliced chicken carries that sauce as both seasoning and the thing that keeps a lean bird from reading as dry. The white sauce is the identity; the smoke is the foundation under it.
The craft happened in the pit before the sandwich was ever assembled. Chicken is leaner than the pork and beef the barbecue belt usually smokes, so the cook is about holding it over wood long enough to take smoke without drying the breast past the point of pleasure. The bird comes off and goes into the white sauce while still hot, because the emulsion has to hit warm skin to cling and the vinegar has to cut the fat while the fat is still soft. The sauce itself is an emulsion problem: mayonnaise as the body, vinegar and pepper and cayenne as the sharp edge, whisked so it stays glossy rather than splitting into oil and water. On the sandwich the bun does what a barbecue bun always does, which is disappear. A plain, soft, slightly sweet bun soaks the sauce and the rendered juice and gives the hands something to hold while the smoked, sauced chicken does the work. A sharp slaw or a few pickles is the standard counter, the acid and crunch a pile of sauced chicken has none of.
The variations stay close to the bird and the bottle. Pulled gives a looser, sauce-soaked sandwich; sliced or quartered keeps more bite and a crisper skin. The same white sauce migrates onto smoked pork and turkey, where it behaves differently against a fattier or milder meat. The dressed build adds tomato and lettuce and pushes it toward a sandwich rather than a barbecue plate in a bun. Each of those is its own preparation and deserves its own article rather than being crowded in here.