While calzones and strombolis are very similar, they have different origins, folding styles, and ingredients, the marinara is served differently, and they use different cheeses.
Calzones were invented in Italy in the 1700s, but strombolis are one of several foods that aren't authentically Italian, hailing instead from the United States in the 1950s.
Calzones were invented to feed working people who didn't have time for a meal, while strombolis were more like experimental stuffed sandwiches that just happened to take off.
Originally meant to be a handheld meal, most calzones today from Italian restaurants are large enough to share. They're meant to look sort of like a pasty or empanada.
The crust starts as a circle, like a traditional pizza pie, then the filling is added to one half. From there, the circular dough is folded in half and sealed.
Created in South Philly, strombolis are handheld sandwich pieces rather than pockets. The dough is shaped into a rectangle, and the filling is added to the dough's center.
Traditional calzones are made without any sauce, with marinara typically served on the side. With strombolis, the dough is topped with a layer of sauce.
Another big difference is ricotta. Traditional calzones should always contain ricotta, while strombolis usually don't have ricotta and almost always contain mozzarella.