Mozzarella in carrozza, mozzarella in a carriage, is defined by the seal. A slice of mozzarella is closed between two pieces of bread, the whole package dipped in beaten egg, and fried until the outside sets into a crisp gold shell and the cheese inside pulls into hot threads. The Naples name is exact: the bread is the carriage, the cheese is the passenger, and the engineering problem is keeping that passenger in. The cheese has to go fully molten while staying trapped, so the sandwich is a controlled fry around a deliberately enclosed centre rather than anything stacked or open.
The craft is moisture control and the seal itself. Fresh mozzarella is wet, and wet cheese steams the crust soft from inside and bursts the carriage in the oil, so the cheese is drained and pressed first until it is dry enough to melt without flooding. The bread edges are pressed together and often sealed with the egg so nothing escapes once it loosens, which is the move that makes this a carriage rather than a leak. Heat is then managed so the exterior colours at the same moment the centre flows, the same timing problem as any griddled cheese sandwich, executed fast and hot for a customer eating it standing. Cut too soon and the centre runs out; the seal has to hold until the first bite breaks it on purpose.
The named turns stay close to the same enclosed-melt idea: the carriage with a salt anchovy hidden against the cheese, and the wider family of the pressed Italian bar toast of ham and cheese that solves the same trapped-melt problem by welding rather than frying. Each of those is the same molten centre in a sealed shell, and each deserves its own article rather than being crowded in here.