So, now that we've covered the three elements as being correlated with mind, body, and spirit, we can establish the dead as lacking one of the three. Some dead people persist through sheer force of will, or ancient rituals, resulting in disembodied spirits (Since we've established that "Spirit" is one of the three parts of a life, we might as well refer to a glob of pure intentions and emotions as a spirit, since that's what we're talking about inside people anyway. It's just weird to see them floating around and going ooooo.) Non-evil ghosts are simply referred to as "the dead." The "Undead" are created when Corruption begins to fill in the gaps. This can be a total replacement (IE: A spirit might gain a body of pure Corruption) or a partial replacement (IE: Ghouls retain most of their body, but the Corruptive process adds claws and other fun stuff.) This can occur naturally when corpses are left in highly Corrupt areas, or via spells and rituals.
Mindless undead are not automatons, and have very limited memories and attention spans. They default to attacking a nearby living uncorrupted creature, moving into a Corrupted area, or wandering aimlessly (here expressed in order of preference.) While undead do not "Tire" in the sense of requiring rest, they do consume energy when they move and act, and require a steady supply of Corruption to sustain themselves in the long term. Gruesome murders and cannibalism are hallmarks of the undead because they are easy sources of Corruption. Zombies and other 'cheap' undead are in particular not ideal vessels for holding Corruption, and thus steadily weaken when removed from a Corrupted domain and denied anything to defile. Better constructed undead, especially mummies, are usually fairly watertight containers, and can safely go dormant for long periods of time without 'leaking' energy.
Vamparism and Lycanthropy are essentially different strains of the same disease, with the former being more spiritually Corrupting and the latter more physically oriented. Both affect all three spheres, however, bringing a suite of changes to their physical, emotional, and mental processes.
Lichdom is achieved via rituals meant to carefully channel Corruption exclusively into the body, in an attempt to achieve immortality without the insanity that accompanies mental Corruption. Of course, playing with pure evil is a very dangerous game, so results are generally mixed. While most liches are spellcasters, the ritual can be performed on anyone, and so-called Death Knights are fearsome indeed. The most successful Liches may seal their mind and spirit inside an object (if they're wise, an indestructible one) which then controls the body as long as it remains within range. The exact range, and the degree of control a Lich can manifest from inside his phylactery both vary wildly between individual Liches. Feel free to have your Lich be a Sauron copy-paste, where he has to be physically touching his phylactery at all times or be reduced to ineffectually glaring, or let him retain full spellcasting ability from inside the phylactery. Maybe the phylactery is a "staff of wonders" that casts spells unpredictably...
Phylacteries are heavily warded to keep the mind from being excessively Corrupted; this shielding also makes them very hard to detect magically. DMs are encouraged to inform the party that not every lich has a phylactery, and that even if this one did, there's very little way to determine which magic item could allow the Dark Lord to return. It's up to them how much treasure they want to throw into a volcano before they feel safe.