As someone mentioned earlier, back in the day. all non-prescription medications were kept behind the counter. Those that were legally sold to all askers were handed "over-the-counter." Those which were more illicit were handed "under-the-counter," which was akin to "under-the-table"

speaking of new york linguistic peculiarities

why does the Bronx get a definite article, when the rest of the boroughs are article-less

furthermore, "downtown" and "uptown" in New York imply the location on the y-axis. In other cities, "downtown" means the commercial/tall-building-ed part of the city, which in New York, is more Mid-town than downtown these days.

that, and in New York "deli" means a place where you can buy beer, cigarettes, lotto tickets, and things like that, and maybe, just maybe, has some twenty-year old lunch meat and stale bread