The difference is the power of the spell. All of the Necromancy spells in Conjuration are tiered, and stronger versions of the spells will cost more magicka and will be able to affect creatures of a greater level.
There's one for each level tier. 1-10, 10-20, 20-30, 30-40 and finally Dead Thrall which reanimates *People* permanently who are level 40 or lower. Anything lower than Dead Thrall (Raise Zombie, Reanimate Corpse, Revenant, and Dread Zombie in order from weakest to strongest) will reanimate both humanoids and most animals for 60 seconds, at the end of which time they turn to ash.