Air Conditioners work with ducted furnace systems. They work by removing the temperature from the air and continually cooling it from there. Best to keep windows and doors closed with this system.
Swamp coolers do not work in tandem with a furnace system. They can be ductless (one opening) or ducted (multiple openings in the ceiling). They add humidity to the air. Works well with windows open.
If you do not have ductwork (maybe you have boiler heat), you can install a wall unit to cool (and can heat areas as well!) particular spaces.