Air handlers and furnaces aren't typically found side by side in Memphis. If you use a furnace, you probably don't need to consider an air handler.
Air handlers are often linked with heat pumps and deliver airflow across your home. Some models also have backup heating and cooling parts to support the heat pump.
A furnace runs differently by blowing heated air into your vents, which circulate it around your home. Because furnaces use combustion chambers to make heated air, they don't need some of the components you'll find in a standard air handler.