The panino farcito is named for an action rather than a recipe. Farcire is the verb for filling, the same word a cook uses for stuffing a bird or a pasta, and a panino farcito is simply a roll that has been filled: the general Italian word for any sandwich that is more than bread. It is the category, not a dish, the term written on a bar sign or a price list to mean "we put things in bread here." What it describes is therefore a principle, not a fixed thing, and the principle is the ordinary Italian one of choosing well and stopping early.
The craft, such as it is, lives in that restraint, because farcire in the Italian register does not mean to overload. A panino farcito is filled with one cured meat, or one cheese, or one cooked vegetable, cut and laid so it reads clearly against the crumb rather than burying it. The bread is matched to whatever goes in: a soft roll for a tender mortadella, a crusted one for an oily salame, a country loaf for a strong cheese, the pairing decided at the salumeria counter rather than the cutting board. Butter or oil appears only where a very lean filling needs a bridge to the bread, and a sauce is the exception, not the rule. The discipline is the same one that runs through the whole Italian catalog: name the thing, frame it, and add nothing that would mask it.
Because it is a category, its variations are the entire tradition rather than a short list. The panino imbottito is the southern register of the same idea, the word carrying a fuller, more padded sense. The place-named rolls, the Bolognese and the Friulano and the Ligure, are each a panino farcito that has declared a region. The integrale version simply specifies the bread. Each of those is a distinct preparation with its own balance to strike, and each deserves its own article rather than being crowded in here.