In the US we refer to the large heater for central air conditioning to be the furnace whether it is gas or electric. The filter is on the blower that pushes the hot air around the house.

The HVAC system.

Depends where in the world you are I think. In the UK most people have combination water/heating natural gas boilers. Some places are on heating oil if you're out in the sticks (or in Northern Ireland which has a different system) and some modern houses are all-electric heat pump setups. We mostly have no air con which is becoming less tenable with climate change, and water-based radiators so nothing like a furnace in American systems.