I am not an expert, but it sounds like you are correct. The contacts in the relay have welded and are in the closed or "on" position. The 110 volt circuit controls the relay, not the DC. That's why turning it off does not stop the DC.
Sometimes you can open a relay or contractor and carefully pry the contacts apart and file of sand them smooth and it will work again. Be sure to turn off both circuits. This is pretty "iffy".
It might be that sawdust or debris has gotten into the controller and will not allow the circuit to open, but that works the the other way most of the time, not allowing it to close. Clean it out.