Air handlers and furnaces aren't usually found together in Fort Worth. If you use a furnace, you probably shouldn’t need to consider an air handler.
Air handlers are usually linked with heat pumps and control airflow throughout your house. Some models also provide secondary heating and cooling components to help the heat pump.
A furnace heats in a different way by sending hot air into your vents, which move it across your home. Because furnaces use combustion chambers to produce heat, they don't have some of the pieces you'll spot in a regular air handler.