Air handlers and furnaces aren't usually used together in Canada. If you use a furnace, you most likely don't need to think about an air handler.
Air handlers are frequently linked with heat pumps and manage airflow around your home. Some systems also offer secondary heating and cooling components to assist the heat pump.
A furnace heats differently by sending heated air into your vents, which circulate it throughout your house. As furnaces depend on combustion chambers to create heated air, they don't have some of the parts you'll spot in a regular air handler.