Spoil and tailings are both wastes. Spoil is the waste left over from mining (i.e., overburden or low-grade rock from the deposit), and tailings are the waste from the processing (i.e., the invaluable part of the ore.)

When one considers a surface mine, piles of spoil usually include the rock that was over and around the ore prior to mining; the particles may be relatively large. Tailings are generated during processing as the valuable minerals are separated from the waste, and the particles are usually small since the ore was ground down to liberate the valuable minerals from the gangue.

Figure: Spoils are the waste left prior to processing the ore.

Figure: Tailings are the invaluable remains after separating/processing the ore.