In the world of Harry Potter, there seems to be a distinction between a ghoul, a ghost and poltergeist.
My understanding is that a ghost is an imprint of a dead wizard, so what are the others and are they related?
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We have detailed descriptions of all three in canon. They appear similar on the surface, but they don't seem to have much in common (other than a propensity for annoying living humans).
From Fantastic Beasts and Where to Find Them:
The Ghoul, though ugly, is not a particularly dangerous creature. It resembles a somewhat slimy, buck-toothed ogre and generally resides in attics or barns belonging to wizards, where it eats spiders and moths. It moans and occasionally throws objects around, but it is essentially simple-minded and will, at worst, growl alarmingly at anyone who stumbles across it.
From the Pottermore entry for ghosts:
In the world of Harry Potter, a ghost is the transparent, three-dimensional imprint of a deceased witch or wizard, which continues to exist in the mortal world. Muggles cannot come back as ghosts, and the wisest witches and wizards choose not to. It is those with ‘unfinished business’, whether in the form of fear, guilt, regrets or overt attachment to the material world who refuse to move on to the next dimension.
From the Pottermore entry for Peeves:
The name ‘poltergeist’ is German in origin, and roughly translates as ‘noisy ghost’, although it is not, strictly speaking, a ghost at all. The poltergeist is an invisible entity that moves objects, slams doors and creates other audible, kinetic disturbances.