The tuna grinder is the New England long-roll reading of tuna salad, and its defining move is heat applied to a cold filling. A cold tuna sub keeps the salad chilled inside the bread; the grinder, in its regional form, is run through the oven or under a salamander with cheese on top until the cheese melts down into the tuna and the roll toasts at the edges. The word grinder itself, the New England name for the long-roll sandwich, carries the expectation: ordering a tuna grinder rather than a tuna sub is, in much of New England, ordering the hot version. The cooking is the point, and it is what separates this from the Philadelphia tuna hoagie's strictly cold logic.
The craft is in the bind behaving under heat and the roll surviving it. The tuna salad lives or dies on its ratio of mayonnaise to fish and on enough acid and crunch, celery, onion, a little pickle, to keep it from collapsing into paste, and that matters more here because warmth flattens a filling that was already dull cold. The cheese, usually American or provolone, is chosen for melt behavior so it flows down into the tuna and binds the loose salad into something the bread can carry rather than sitting on top as a separate sheet. The grinder roll is the structural component: a long roll with a crust firm enough to take a wet, warm filling and a brief bake without folding in the middle, split and layered the length of it so every bite holds the whole sandwich. It is toasted only long enough to set the cheese and crisp the crust, because a longer bake dries the tuna and shatters the roll. The cool accents, shredded lettuce, tomato, sometimes raw onion, are added after the heat rather than baked, so they keep the crunch the warmed filling has lost.
The variations are mostly the heat decision and the regional name. The same tuna run cold and undressed by the oven is a different sandwich that happens to share a filling; the Philadelphia tuna hoagie is the cold build under another name; the tuna melt takes the same logic onto sliced bread under a griddle. It sits in the broad sub, hoagie, hero, and grinder family, one architecture wearing local accents, where the roll is the engineering and the filling is the variable. Each of those is its own build and deserves its own article rather than being crowded in here.