The egg salad grinder takes a filling that was built for soft bread and forces it onto a New England sub roll instead, and the swap is the whole sandwich. Egg salad has no structure of its own: it is chopped hard-boiled egg bound in mayonnaise, a cold paste that brings flavor and zero load-bearing ability. Put it on a long roll meant for shingled cold cuts and the roll has to do all the work that the filling cannot, which is why this reads as a different thing from the same salad on sliced bread. The grinder roll is the reason it holds.
The craft is in matching a loose bind to a sturdy carrier. The roll is a Northeastern sub length with a crust firm enough to keep its shape under a wet center, and at the diner counter it is usually split and warmed or lightly toasted so the cut faces firm up before the salad goes in. That toasting is deliberate: a cold mayonnaise bind soaks a raw crumb fast, and a warmed face buys the sandwich enough time to survive the trip from the cutting board to the table. The egg has to be chopped coarse rather than mashed, so there is texture against the give of the roll, and the bind kept tight enough that it does not run out the open ends when the sandwich is picked up. Lettuce or a few rounds of tomato go in as the cold, crisp counter to a filling that is otherwise one soft note, and the salt is carried in the bind because the roll will dilute it across that much bread.
The variations stay inside the diner idiom. A version folds in crisp bacon for smoke and crunch; another lays American cheese against the warm roll so it slumps into the salad; a third leans on celery and pickle relish for sharpness against the fat. Curried egg salad on the same roll shifts the whole register. Each of those is its own build with its own balance, and they deserve their own articles rather than being crowded in here.