Air handlers and furnaces aren't often found together in Birmingham. If you rely on a furnace, you likely shouldn’t need to think about an air handler.
Air handlers are frequently paired with heat pumps and manage airflow around your home. Some units also provide extra heating and cooling parts to help the heat pump.
A furnace heats differently by blowing heated air into your vents, which move it around your home. Since furnaces depend on combustion chambers to produce heat, they don't need some of the parts you'll find in a normal air handler.