Spirits may be ghosts (souls back from death to aid or punish the living) or supernatural beings who decide to interfere in the mortal world. They usually can fly as they have an incorporeal body. Their power varies from meek dwelling spirits, to mighty, legendary entities.
The Kami are the gods of Kamigawa. There's a kami for every thing or aspect in life, varying greatly in power. During the Kami War, millions of kami invaded their world in a crusade against the mortals.
Ghosts of Ravnica
Geists of Innistrad