The chip butty with gravy is the Northern English wet finish on the plain chip butty, and the gravy is doing something the curry-sauce and mushy-pea versions do not. Where curry sauce is sweet and mushy peas are a soft bed, gravy is savoury and thin and meaty, and it soaks rather than sits. Hot chips go on thick-buttered soft white bread, brown gravy is poured over them or served alongside for the bread to be dipped into, and the bread is closed and pressed. The defining fact of this version is absorption: the bread is meant to take the gravy up, not resist it, and a chip butty with gravy that has stayed dry has failed at the one thing that separates it from a plain one.
The craft is controlling how far that soak goes before the sandwich collapses. Gravy is thinner than curry sauce and runs faster, so the butter underneath stops being optional and becomes a deliberate barrier: spread to the edges it slows the gravy reaching the bottom crumb long enough for the butty to survive being picked up, while still letting the top of the bread drink enough to turn savoury and soft. The chips have to go in hot so the gravy stays loose enough to coat them and the fat of the chip and the gravy emulsify into a single brown slick rather than separating into greasy chip and watery sauce. The bread is plain and soft because a crust with chew would resist the gravy and the whole point is bread that gives way; the only firm note in the build is the crisp edge the chips keep for the first few bites before the gravy reaches them. Dipping the butty into a pot of gravy rather than pouring it over is the same sandwich engineered to keep the chips crisp longer, the soak put under the eater's control.
The variations are the same chip-and-bread spine with a different wetting agent or an addition to the gravy. Curry sauce is the sweeter Southern-tilting alternative; mushy peas are the soft-bed version rather than a sauce. Onion gravy thickens the build and adds a sweet allium note, cheese melted into the chips under the gravy is the loaded form, and a gravy butty with a few scraps of roast meat folded in pushes it toward a leftover-dinner sandwich. Each deserves its own article rather than being crowded in here.