Ghouls and Skaabs
Zombies In Innistrad
In Innistrad, and Magic the Gathering in general, zombie is a much broader term than in most Dungeons and Dragons settings. In general, the term can be applied to any undead creature that is corporeal and fleshy but obviously dead. Ghosts are spirits, vampires are always called vampires, and anything that is bare bones or nearly so, is called a skeleton.
Everything else, from hordes of severed limbs, to multi-armed half-decomposed corpses, to hulking brutes with giant maces grafted in place of their fists, is a zombie.
Innistrad, however, has two distinct classes of zombies- Ghouls, animated by pure necromantic magic and a powerful incantation which give their creators the name Ghoulcallers, and Skaabs, animated by mad necro-alchemists called Skaberan with science, alchemy, and magic in concert.
In general, spells that create undead creatures are the domain of ghoulcallers, while Skaabs are made with the necromantic feats of the Tome of Necromancy.
Crazed, desperate, or foolhardy Black and Blue characters may have their heart replaced or augmented by a ghoulcaller or skaberan that they trust, or have paid enough to reasonably ensured won't cheat them. This confers many benefits of being undead without actually being undead. The character benefits from Medium Fortification, gaining a 75% chance to ignore critical hits and sneak attacks, heals from negative and positive energy (albeit at 50%), and needs only 25% the normal amount of sleep and food.
The skin of a Zombiehearted character is slightly greyed, and they have a large, obvious scar on their chest where their heart was accessed.