In New England the meatball sandwich is a grinder, and the name is a working description, not a regional flourish. The defining move is the second trip to the heat. Meatballs in marinara are loaded into a split roll, mozzarella is laid over the top, and the whole assembly goes back under a salamander or into the oven until the cheese blisters and the roll edges go hard. A grinder is not a cold sandwich warmed by its filling; it is a sandwich that is finished hot, with the bread toasted around a sauce that would otherwise drown it. That run-back-under-heat is the entire point, and it is why a grinder roll has to start sturdier than a roll built for cold cuts.
The craft is in defending the bread against the sauce for the length of the sandwich. The roll is split most of the way through but left hinged, so it holds the meatballs in a trough rather than letting them roll out the side. A light toast of the interior before the meatballs go in seals the crumb so the marinara sits on a crust instead of soaking straight through. The meatballs are sauced but not flooded: enough marinara to keep them from going dry under the heat, not so much that the roll gives way before the last bite. The mozzarella does structural work as well as flavor work, melting into a lid that holds the meatballs in place and keeps the open face from steaming itself soft. Timing is the whole skill, the cheese fully molten at the moment the roll reaches deep gold, the same patience problem a griddled grilled cheese poses, solved hotter and faster.
The variations stay close to the oven. Provolone in place of mozzarella sharpens it; a layer of sauteed peppers and onions turns it toward a sausage-and-peppers build; a heavier hand with grated hard cheese under the broiler pushes it toward a parm. Some shops grind their own beef and pork blend and bake the meatballs in the sauce so they take on its seasoning; others fry them first for a firmer outside. The Philadelphia hoagie, the New York hero, and the national meatball sub run the same meatballs through their own local rules, and each of those deserves its own article rather than being crowded in here.