Same with my family. It was an Italian-American convention in the Bridgeport/Stratford area where I grew up. As best as I have been able to tell, this was simply our way of ordering a cheese pizza, with Italians-Americans who (or whose families) had immigrated from the Naples area calling the cheese "scamozz." I'm almost certain it was always mozzarella cheese here, but there is a regional variant in Italy called "scamorza," which is similar to mozzarella (it is both smoked and unsmoked, but in some areas they use the term only for the smoked variant). You can find scamorza here, but it is not common (and never has been) and would be much more similar to fresh mozzarella, not the low-moisture, part skim mozzarella used by most pizza places on a standard cheese pizza, which is what I remember us getting when we ordered a "scamozz apizza."
Portofino is the best and most consistent in town imo, especially if you're in North Madison, Dove. Red Tomato is actually Madison, too, but it is near the Guilford line. It is good, but it's not New Haven, and not worth the inconvenience as compared to Portofino imo. It also doesn't travel all that well in my experience. Portofino's new restaurant in New Haven just opened last week. It is called "Da Legna" and it is on State Street, where Abate's Pizza used to be (across from Christopher Martin's). I have not been yet, but we are going for dinner next weekend and I will report back. He has a wood-fired brick oven imported from Italy for the pizzas, and he has teamed with talented New Haven area chef Dave Foster, who is making several small plates and salads. I'm looking forward to it. BTW, if you haven't had them yet, Portofino's stuffed breads are ridiculously good. Just don't start bringing them to other people's houses for gatherings, because they'll never ask you to bring anything else, and their "order" will double every time, as people wipe the things out in no time.
Nuzzo's is okay, but nothing really special imo. We use them because our kids like them, and when we need delivery. IMO, the next best local option besides Portofino is Bradley and Wall. Their sauce in particular is excellent; I think their use of plum tomatoes is the difference. Give them a shot next time. Their entrees, sandwiches and sides, etc. are also good.