what is the difference between motherboard speed and the processor speed for computers such as the 80386DX

Question

Your use of the term "motherboard" speed is outdated. I assume you mean motherboard bus speed. Processor speed can be higher than that, and normally, it is a fixed integer speed multiplier, say like 16x, fixed multiple. On the 80386DX, all the variants clocked the bus speed the same as the processor. One version did this all the way up to 40Mhz. So the fixed muliplier was 1:1 on that chip series. The 386 did not offer much improvement over the 286, but the 386 did allow graphical user interfaces on Windows, which is now standard.