Air handlers and furnaces aren't usually installed together in Canada. If you use a furnace, you probably don't need to think about an air handler.
Air handlers are typically used with heat pumps and manage airflow across your residence. Some systems also have secondary heating and cooling components to assist the heat pump.
A furnace runs differently by pushing warm air into your vents, which circulate it throughout your house. Because furnaces depend on combustion chambers to create heated air, they don't have some of the parts you'll spot in a standard air handler.