The chicken salad sandwich is decided entirely before any bread is involved, in the bowl. Cooked chicken is chopped and bound with mayonnaise, celery, and seasoning, and the quality of that bind is the whole sandwich, because nothing in the assembly afterward can fix it. This is a bound-salad sandwich, which means it belongs to the lunch-counter family that proves how little a sandwich needs: a good filling, a soft slice, and a clean diagonal cut. The restraint is the design. There is nowhere to hide a dry bird or a gluey mix behind four ingredients.
The craft is a ratio problem with two failure modes. Too much mayonnaise and too fine a chop and the filling reads as paste; too little binder and too coarse a chop and it falls off the bread in dry chunks. The fix is structural, not seasoning: enough acid and crunch, from celery and often pickle, onion, or grape, to keep the mix from being one soft note, and a chop that leaves the chicken in pieces with chew rather than shredding it to thread. The bread is deliberately soft and neutral, white or a light wheat, because a crust with real bite fights a filling that has none, and the point of the sandwich is the filling. Lettuce is doing a job, not decorating: it is a cool, crisp barrier that also keeps the wet salad off the bread long enough to get the sandwich from the counter to the hand without the slice giving way.
The variations are small and honest, which is the nature of this shelf. Roasting the chicken instead of poaching deepens the base; folding in tarragon, curry powder, or toasted nuts and fruit turns it into a recognized regional or tearoom style; serving the same bound salad on a croissant or in a pocket changes the carrier without changing the idea. The egg salad and tuna salad sandwiches are the same engineering problem with a different protein. Each of those is a codified build with its own logic, and each deserves its own article rather than being crowded in here.