I’ve never heard of mozzarella on a combo. A combo is an Italian sausage nestled in an Italian beef, as I’ve always known it. That’s how Johnny’s, Al’s, Pop’s, Portillo’s, etc., does theirs. Never heard of it being covered with baked mozzarella cheese, but there are “cheesy beefs” out there, so I wouldn’t be surprised if there’s some sort of “cheesy combo,” too.
Anyhow, to explain what an Italian beef is. It starts with roast beef. Top sirloin, top round, or bottom round are the usual cuts. It is then very thinly sliced–the exact level of thinness depends on the joint. Some slice it thin enough so it falls apart. Others enough to hold its shape, but it shouldn’t be much thicker than your typical deli meat. It is then dipped to finish warming/cooking in a flavorful beef broth/jus. Typically, you’re looking at a fairly salty beef broth, redolent with Italian herbs and spices, and garlic. It is then served in a sturdy Italian roll.
You can get it dry, wet, or dipped. With “dry” the beef is removed from the jus, excess moisture drained, and served on the bun. “Wet” it is directly taken from the jus to the roll. “Dipped” is wet, with a dunk of the whole thing into the jus. For me, “dipped” is the only way.
Furthermore, the other option, besides “dry/wet/dipped” is “sweet/hot/no peppers.” Sweet gets you griddled green peppers with your sandwich. Hot gets you giardiniera, a pickled condiment of olive oil, vinegar, hot peppers, celery, carrot, cauliflower, olives, garlic, etc. At its very simplest, it can be just basically be pickled hot peppers and celery, but more usually it includes the above. You can also opt for “hot & sweet,” (my favorite) which is the griddled peppers with giardiniera. Or you can just go for no peppers at all.