The roast turkey sandwich is defined by a problem the other roasts do not have, which is dryness. Turkey is a lean bird with little marbling, and what fat it has does not carry through the breast the way pork or lamb fat does. Roasted and then left to go cold, the meat firms and tightens and gives up most of what little moisture it held, so a turkey sandwich built carelessly is dry, pale, and flat in a way a beef or pork sandwich is not. Everything that makes this sandwich good is a response to that. The defining decision is not which cut to use but how to put moisture and savour back, and the standard answer is a wet, sharp condiment doing the work the gravy did on the plate. The turkey supplies the body; the moisture is the whole craft.
The build is an exercise in lubrication. Cold turkey is sliced thin and against the grain so each piece stays tender rather than going to dry rope, and the cut is laid loose rather than packed tight, since dense layers of a dry meat read drier still. A wet element runs through the sandwich rather than beside it: cranberry sauce for sharp fruit, a generous mayonnaise, or a smear of stuffing carrying its own moisture and salt. The bread is buttered to the edges, which here is not only flavour but a moisture barrier the other way round, keeping a sauce from the crumb while still bridging the meat to the wheat. The bread itself can be softer than a beef sandwich would take, because there is no heavy fat to fight and the priority is a yielding mouthful rather than structural strength.
The variations are almost entirely a Christmas inventory and a question of which moist counter is chosen. Turkey with cranberry is the sharp-fruit standard; turkey with stuffing and a smear of sauce is the leftover Christmas sandwich in full; turkey with mayonnaise and a little black pepper is the plainest working version that still solves the dryness. The hot turkey roll run with gravy belongs to its own tradition. Each deserves its own article rather than being crowded in here.