A furnace is an appliance that generates heat for a building by burning fuel, then distributes the heat through ducts into the rooms of the building. An air handler is an appliance that blows heated or cooled air through ducts. Installed in a home, these two devices can look very similar, which leads many people to refer to the air handler, incorrectly, as a "furnace."
Whether a home has a furnace or an air handler depends on the kind of heating system it has. If you heat your home with gas, liquid propane or heating oil, you probably have a furnace. If you have an electric heat pump, you probably have only an air handler.
A furnace has four main parts: the burner or combustion chamber, where natural gas or another fuel is burned; the heat exchanger, where the heat from the burner—but not the potentially dangerous gases produced by combustion—transfers to the home's air supply; the blower, which forces the heated air through ducts into the home; and the flue or vent, which carries combustion gases such as carbon monoxide to the outside.
Some furnaces heat water, not air, for use in radiators or steam pipes. These furnaces are usually referred to as "boilers."
Air handlers work in conjunction with a heat pump, a device that uses refrigerants to move heat energy from one place to another. The handler has a blower that forces air through the house, and the refrigerant lines run through the air stream just "downwind" from the blower. During the summer, the refrigerant pulls heat out of the air steam and moves it outside; the result is that the air handler blows cool air. In the winter, the refrigerant pulls heat energy from the outside air—yes, there is heat energy even in cold winter air—and moves it inside, with the result being that the air handler blows warm air. The air handler is not heating (or cooling) the air. It's just blowing the air past the refrigerant lines, which are changing the temperature. That's what makes an air handler different from a furnace.
For homes with both a furnace and central air conditioning, the furnace's blower acts as the air handler for the air conditioning system.
To maintain air quality, both furnaces and air handlers have filters that capture dust and other impurities out of the air. Filters must be replaced regularly to ensure that the appliance works efficiently. Both also continually mix air from the outside into the stream of air circulating through the home.
Both a furnace system and a heat pump/air handler system are controlled by thermostat.