Crab and chive is one of the lightly dressed crab sandwiches, and what separates it from its siblings is the herb. Picked crab meat is bound in a mayonnaise carrying chopped chive, so the dressing brings a thin, green, mild-onion note worked all the way through rather than dropped on top. The chive is not a garnish scattered for colour. It is folded into the bind so every forkful of crab carries the same gentle allium lift against the meat's sweetness. That integration is the whole sandwich. Take the chive out and you have plain bound crab, which is a different and flatter thing.
The craft is dressing the crab enough to hold it without turning it to paste. Crab meat is delicate and breaks down fast under a fork, so it is folded gently through just enough chived mayonnaise to make it cohere, never beaten smooth, because a crab sandwich that has lost its flake has lost the texture that makes it crab. The chive is cut fine and used in a measured amount: enough to read as a clean onion note, not so much that it overrides a meat whose entire appeal is its sweetness. White meat keeps the filling pale and mild, a little brown meat deepens it, and the balance is a matter of how rich the sandwich is meant to be. The bread is soft and plain, usually brown, and buttered to the edges so the crumb is sealed against a filling that carries its own moisture and so nothing competes with a flavour built on lightness. Cut thin and not overfilled, it is a sandwich that depends on the crab being good and the chive being restrained.
The variations are the rest of the dressed-crab shelf, each defined by the single note worked against the meat. The plain crab sandwich runs white and brown meat with only lemon and butter; crab and lemon swaps the herb for bright acid in the bind; crab paste takes the same shellfish to the concentrated, shelf-stable end of the larder. Each deserves its own article rather than being crowded in here.