A spirit is a soul that was formerly a human that passed away. Depending on what kind of life the spirit led while they were alive and how they died, their destination in death may be to a peaceful place, probably Heaven (in the case of Elise, who remarked that she had indeed come from Heaven to help Josh and Carl defeat Parker and Michelle Crane) or to a dark dimension known as the Further or to Hell.
The tortured ghosts that are lost inside the Further are seemingly damned to endure a miserable existence forever, roaming the Further or reliving their painful memories, unless an astral projector travels in the Further by mistake, which allows a spirit to gain another chance at life. However, this takes time and spiritual energy to do and may cause the physical body to decay if successful.
Apparently, spirits not necessarily have to be all condensed into one manifestation, Parker Crane's younger self helps Carl, Elise and Josh in order to end his mother's tyranny while the conscious Parker, who is now in possession of Josh's body, is trying to murder Josh's family. As Elise seems to insinuate when she exhorts Josh to destroy Michelle Crane's memories, spirits are clusters of memories from those they used to be while they were alive. Perhaps, those who suffered very traumatic experiences may have their memories split, which results in distinct and simultaneous manifestations of themselves.
A demon is a fallen angel that was cast out from Heaven eons ago along with Lucifer. They are dark, satanic beings that are usually portrayed as malevolent, sinister, evil, wicked, and sadistic. So far, there are only two known demons that lives in the Further: The Lipstick Demon, sometimes called the Red-faced Demon or simply the Demon, and the Wheezing Demon. While the Long-Haired Fiend is sometimes called the Long-Haired Demon, it is unknown whether he is actually a spirit or lesser demon, although it seems likely he is the former.
While demons are also spirits that can be found in the Further, they are a minority among the hordes of dead human spirits lurking in the spirit realm. However, they are usually much more powerful than any other entity, including Travelers, who despite being mightier than other human spirits by virtue of actually being alive, cannot contend with a Demon.
Such spirits might include: