A relay relays electrical power to the heating elements and blower motor inside the furnace cabinet, and then the heating elements then provide the heat that warms the air, and the blower motor sends warm air through the ductwork. A transformer transforms electrical energy from one circuit to another, or to multiple circuits, alternating the current from one voltage to another. Transformers take up a lot of space, so choose a relay without a transformer if you need to save space.