In my experience, a regular sandwich and an Italian sandwich are two quite different things. A regular sandwich is typically American in nature, with meats, cheeses, dressings and toppings that reflect this culture. It's classic in that sense, but ultimately it's always the same. An Italian sandwich, on the other hand, is much more varied in its ingredients and can vary greatly depending on where you are.
In South Jersey, where many other sandwich stores sell sandwiches, if you walk into their store and order a sandwich, they'll jokingly remind you that you've crossed the bridge and that you're now in Jersey and it's called a Sub. Family restaurants in the South Philadelphia neighborhood began offering Hoagies as a stand-out sandwich, and Wa Wa Food Markets began selling hoagies in the late 1970s. Philadelphians who began migrating to South Jersey in the 1950s kept the name Hoagie for the popular sandwich. But a tuna sandwich like Chickie's, in South Philadelphia - a sandwich roll with tuna meat, roasted Italian vegetables, aged provolone and olive oil - is not a hoagie.
New Jerseyans love their food and the most popular sandwich in New Jersey is the Italian sandwich, although it's not called an Italian sandwich - depending on what part of the state you live in, it's called a Hoagie, Hero or Sub. You can better describe the differences between a hoagie and a sandwich by understanding that a hoagie is a type of sandwich. A hoagie roll with tuna salad, shredded lettuce, sliced tomato, and sliced onion isn't really a hoagie.