If so, can I buy the relay separately or is it part of the control board?

It would depend on the model of the furnace. The only relay needed in the air handler is the fan relay, the other parts are for time delays. High efficiency gas furnaces have a time delay to run the blower a while to extract all of the heat from the heat exchanger, but with a $5.00 time delay or an adjustment of the fan switch attached to the heat exchanger the circuit board can be replaced unless you have a two-stage gas valve. Air handlers are really very simple to configure. Give us the model number and maker and I can advise you better.

See attached picture. It has a variable speed motor which has stopped working. The furnace is 5 years old. Thanks a lot!

Give us the model and serial number of furnace and the manufacturer and I can tell you more, but it looks like the fan relays are on the circuit board which are the two black boxes. It could be that one relay is a fan relay while the other one is to something else. It would be easy to substitute all that for a $10 relay or two. A circuit board's price can be very high. [email protected]

Pictures attached