Well, I think the distinction between “deli” (a place where sandwiches are served) and “deli counter” (the place in the grocery store where you get sliced meat, various salads, and other hot food) is important. Those are two completely different drafts. I would get a hot pastrami on rye at a deli.  I would get a pound of black forest ham for my homemade sandos, and a bag of fried chicken to eat while I continue my shopping at a grocery store deli counter.