The patty melt is not a cheeseburger, and the difference is the bread and the griddle. A thin beef patty, Swiss cheese, and a heap of slow-caramelized onions go between two slices of rye, and the whole assembled sandwich is griddled in fat like a grilled cheese rather than stacked on a soft bun. That is the defining move: the patty melt borrows the burger's center but submits it to the grilled cheese's method. The rye is not incidental. Its faint sourness and tight crumb stand up to the fat and sweetness inside in a way a soft bun never could, and the caramelized onion, not lettuce or tomato, is the burger's reimagined garnish. The sandwich is a burger that decided to become a melt.
The craft is heat management on two fronts at once. The patty is pressed thin so it cooks through fast and lies flat under weight, because a tall burger patty would keep the bread off the griddle and the cheese from melting evenly. The onions are cooked low and long until they collapse into something sweet and jammy, and they double as the moisture and the counter to the rye's edge. The cheese has to be fully molten at the same instant the rye reaches deep gold, the same unforgiving timing that defines grilled cheese: rush it and the bread scorches over cold cheese and an undercooked patty. The rye is sturdy enough to crisp and carry a heavy, fatty load without going soggy. A diner flat-top is built for exactly this, the onions held warm in a corner, the patty smashed to order, the whole thing pressed and flipped until both faces lacquer.
The variations stay inside the griddled-rye frame. Some builds swap Swiss for American for a looser melt, or trade rye for sourdough, which softens the sharp counter that defines it. The patty melt belongs to the same family as the tuna melt and grilled cheese itself, all of them governed by the same low-and-patient griddle logic, and it sits one step from the American burger, sharing its center but not its bun. Those are their own sandwiches with their own rules and deserve proper articles of their own rather than being crowded in here.