A haggis supper roll is the chip shop's haggis put into bread, and the word that matters is supper. In a Scottish chippy a supper is a fried main with chips, so a haggis supper is a slice or round of haggis dropped into the fryer in batter or breadcrumb, lifted out crisp, and served with chips. The roll takes that whole hot fried unit, sometimes the chips alongside it as well, and folds a soft morning roll around it. The defining move is not the haggis on its own but the frying: a spiced oat-and-offal mixture that is already cooked is given a brittle deep-fried shell, and that crackling crust against a yielding roll is the entire reason the thing has its own name rather than being a plain haggis roll.
The craft is heat and grease management, the same problem every chip-shop sandwich poses. The batter or crumb has to come out of the fryer crisp and stay crisp for the few minutes it takes to reach the hand, so the haggis goes in straight from hot and the roll is soft and faintly absorbent, chosen to take a little of the fat without turning to paste. Haggis carries its own pepper and spice, so no sauce is structurally needed, though brown sauce is the usual Scottish answer and goes inside in a measured stripe rather than a flood that would steam the crust soft from within. If the chips go in too, they are the soft starch bed under the fried haggis, and the roll has to be generous enough to close over both without the whole thing splitting along the side.
The variations stay inside the chip-shop frame. A haggis roll with the haggis warmed and not fried is the plainer parent, soft against soft, no crackling shell. The same supper logic runs across the whole fryer: a black pudding supper, a white pudding supper, a sausage supper, each a fried main folded into the identical roll. Add a fried egg or a scoop of neeps and tatties and it reaches toward a full plate carried in one hand. Each of those is its own sandwich and deserves its own article rather than being crowded in here.