Air handlers and furnaces aren't often found together in Houston. If you rely on a furnace, you likely shouldn’t need to consider an air handler.
Air handlers are usually linked with heat pumps and manage airflow throughout your house. Some units also offer backup heating and cooling pieces to support the heat pump.
A furnace works differently by sending heated air into your vents, which send it around your residence. Because furnaces have combustion chambers to create hot air, they don't use some of the parts you'll see in a regular air handler.