The soft-shell crab sandwich is defined by the fact that the whole animal goes in, shell and all, legs hanging off the bread. A blue crab caught just after it molts has a shell soft enough to eat, so the crab is cleaned, dredged, and pan-fried whole rather than picked for its meat. Nothing about this is a crab cake. There is no binding, no forming, no patty: the structure of the sandwich is the crab's own body, fried crisp on the outside and sweet and custardy inside, and the bread is there only to hold something that already has its own shape.
The craft is in the fry and the timing. A soft-shell crab is mostly water and delicate meat under a thin shell, so it is dredged lightly and pan-fried hot and fast in butter or oil, just long enough to crisp the shell and set the interior without overcooking it to rubber. It is built immediately, while the shell still crackles, on plain soft white bread or a soft bun, because a crusty roll would fight a fragile fried crab and a slow assembly would steam the crispness away. Tartar sauce supplies the acid and fat the crab does not, and a leaf of lettuce or a slice of tomato adds the cool counter, but the build stays deliberately spare so the crab is the entire event. The legs are left to overhang the bread on purpose; trimming them to fit would mean cutting away the part that proves it is the whole creature.
The variations stay close to the season and the shell. A remoulade build swaps tartar for a sharper, spiced sauce; a Chesapeake version dusts the dredge with the regional seafood seasoning before frying; a po' boy build runs the same whole fried crab on light, crackly Louisiana French bread. The wider American fish-and-shellfish sandwich family, the fried fillet, the crab cake, the regional lake and Gulf builds, shares the logic of defending a crisp coating inside a soft sandwich, and each of those deserves its own article rather than being crowded in here.