The Yorkshire pudding wrap is defined by its wrapper. A Yorkshire pudding is a batter of egg, flour, and milk poured into hot fat and baked until it puffs into a crisp-edged, hollow shell; cook one large and flat instead of in small tins and it becomes a pliable round big enough to fold around a filling. The novelty, and the whole point, is that the containing bread is not bread at all but roast-dinner batter, and the filling it is built to carry is a full Sunday dinner: sliced roast meat, roast potatoes, stuffing, vegetables, and gravy, folded into a single hand-held parcel. It is the roast made portable, with the component that normally sits beside the meat promoted to the thing that holds everything together.
The craft is the pudding and the load. A wrap-sized Yorkshire has to be baked thin and supple enough to fold without shattering, which is a different bake from a tall, crisp individual pudding, so the batter is spread wide and cooked to set rather than to maximum rise. The filling is hot and heavy and includes gravy, so the pudding is folded and eaten quickly before the sauce soaks the batter soft and the parcel gives way, and the components are packed tight along the centre so the fold closes around them rather than letting them slide out the open end. The gravy is the binding element and the risk at once, which is why this is street food eaten on its feet, not a thing left to sit.
The variations track the carvery. A beef-and-horseradish build leans on the classic roast pairing; pork with apple sauce and crackling, or turkey with stuffing and cranberry, swap the meat and its defining sauce while keeping the batter wrapper; the conventional wrap does the same containment trick with an ordinary flatbread instead of a pudding. Each deserves its own article rather than being crowded in here.