You are forgetting that the relay has to handle a closure into a short circuit and survive long enough for a protective device to open. This generally means you use a small 5A mains rated relay on the board and use that to drive a proper 16A or 25A mains motor rated contactor, with double break contacts so that it will still open even if the one contact has welded shut. The contactor is not a board mount component, it is mounted either on a DIN top hat rail or bolted into place in the enclosure. Driving a heater load is only a little worse than driving a motor, you just do not have a large power factor correction current to deal with, but have the same requirements for isolation distance when contacts are open, double break contacts and overload capacity. these are generally available with various coil ratings, 12VDC, 24 VDC, 24 VAC, 48VDC, 110VDC, 220VAC and 380VAC. Typically not available in a latching configuration, and all will typically draw 3-5W of coil current when energised.