Undead is a loose term describing bodies or spirits that rise from the dead.Immortal souls (like those of the Elves or immortal Orcs) usually were drawn to the West to rest in the Halls of Mandos, however if these Souls feared punishment for committed sins or did not repent they could try to escape and hide in the mortal Lands.These spirits were usually incorporeal and existed only within the Spirit World.Souls of Mortals (Men, Hobbits, mortal Orcs) however usually strove to leave Arda and travelled to Illuvatar within the timeless Halls.By Black Magic however this drive might be delayed or hindered or the spirit could become tied to a part of the substance of Arda (A mighty magical artifact like a Ring of Power, a Morgûl-Blade or the Stone of Erech). These Spirits were still destined to leave to the timeless halls, however they could not leave until the bane was broken.
A third category of Undead were spiritless bodies, corpses, that had become animated by a powerful will, either of a Magician who forced the dead body to move, or an incorporeal spirit (either of Ainur origin or the fleeing soul of an Elf or immortal Orc) who took the dead body as his new home.
Finally Undead or Ghosts also could also just be simple Illusions or Phantoms, scheme-like memories of spirits long gone.
The Spirits of dead Dwarves usually wandered to the Halls of long Waiting within Mandos and could not be reduced into Shadows, even by magical artifacts like Rings of power.However in theory their dead bodies still could become occupied by wayward spirits of other origin.
Bound Souls (Bodies whose spirits strife to the Halls of Mandos but are yet bound by a greater power for example the Stone of Erech, the Nine Rings of Men or a Morgûl-Blade).
