The Publix Cuban sub is a Cuban sandwich as read off a supermarket deli case, and that origin, not the fillings, is what defines it. A true Miami Cuban is decided by the plancha: the press is the recipe. The deli-case version inverts that. It is built to order from sliced Boar's Head ham, roast pork, and Swiss with pickle and mustard on a soft French loaf, and it is most often handed across the counter cold, pressed only if the eater asks. Read cold, it is a stacked sandwich whose components have to stand on their own without the heat and weight that fuse a real Cuban into one thing. That is the honest shape of it: a Cuban's parts list assembled by a deli slicer rather than a Cuban's defining technique.
The craft is in the slicing and the bread, because without the press those carry the sandwich. The ham and pork are cut to order rather than pre-portioned, which keeps the cured edge pliant instead of dried, and they are shingled the length of the roll so each bite delivers both meats rather than a band of one. The bread is a soft French sub loaf with a thin crust and an airy crumb, chosen because it will compress cleanly if it is pressed and stay tender if it is not, where a hard roll would refuse both. The Swiss goes against the bread so that, pressed or not, it tacks the structure together, and the thin pickle slices and the smear of yellow mustard supply the single sharp acid that keeps the doubled pork from reading flat. Pressed on the deli flat-top, it moves toward the Florida Latin original: the cheese fuses, the loaf flattens, the pickle drives into the fat. Cold, it is a cured-pork-and-Swiss sub that names a Cuban without performing one.
The variations are mostly the press decision and the cheese, chosen at the counter, plus a wrap version and a build that adds salami in the Tampa manner. These sit inside the broad Cuban and Florida Latin family, where the medianoche runs the same fillings on a sweeter egg roll, the pan con builds carry a single meat on the same bread, and the tripleta stacks three meats in the Puerto Rican manner. Each of those is a codified build with its own partisans and deserves its own article rather than being crowded in here.