Hams, whether city or country, can be smoked or unsmoked. Country hams are salt cured and then aged to remove moisture and develop flavor. This traditional process takes a lot of time. Think prosciutto, serrano, jamon iberico, or American style country hams. City hams, by contrast, are cured by injecting them with brine. This allows rapid salt/nitrite penetration and yields a faster, wetter, less salty product. Honey Baked Ham is probably the biggest name brand for this type of ham, and many other brands have a similarly sweet profile (but not all city hams are sweet hams). City hams are ready to serve from the get-go, but if you're going to cook and serve a whole country ham, you often need to soak it to leech some of the salt out or it can be unpalatably salty.
