Both burrow in the lawn. Voles leave tunnels. Moles leave volcanoes and tunnels.
Voles eat the roots of plants for the most part.
Moles eat grubs, earthworms and just about any insect they can catch. These are battery powered, humming devices that when stuck in the ground, drive the rodents nuts with the continual noise and vibration. The theory is that the rodent can 't hear its prey with all the background noise, so it leaves the area. Hard to do with voles. In any case, reduced grubs mean a healthier lawn.