I found a detailed article written for two classes taught by Carl and Keith Johnson from The Atlantic Paranormal Society about categories of hauntings. There are basically three types: "human", "residual" and "inhuman". This post is like a Cliff's Notes version. Read the article if you want to know more about these types of hauntings.
A "human" or "intelligent" haunting are entities (known as spirits or ghosts) that possess limited human personalities and emotions. They appear in human form and respond to activities of the occupants of a household, the presence of investigators, or the rearranging of furnishings in a setting. They are attached to particular sites, vicinities or dwelling places, usually houses. EVPs and pictures/video of "orbs/globules" are the type of evidence that can be captured with this type of haunting.
The second type is called a "residual" haunting. In this case, a scene from past or present replays itself and is witnessed by a living person(s). They rarely acknowledge any present day observers. Known "residual" apparitions include Ann Boleyn and Katherine Howard at the Tower of London where they were both imprisoned prior to being beheaded. Marie Antoinette, who was also beheaded, has been seen sketching on the front lawn of her Paris estate. There has been speculation that some UFO sightings are also examples of "residual" hauntings. Instead of seeing scenes of the past or present, you see a glimpse of the future which is the idea of clairvoyance and precognition.
There has been much debate in this last haunting. A "demonic" or "inhuman" type of haunting is perhaps of other-dimensional origin, and is often possessed of a quite hostile nature. It's similar to a "human" haunting as it evinces a form of intelligence as in it anticipates the approaches of a person it menaces. It usually occurs in households of psychological instability, distress or unresolved conflict on the part of a resident(s) who perhaps inadvertently invited the demon through scrying implements such as a Ouija Board, conducting séances, indisciplined psychic experimentation, performing magic ceremonies or by habitually conversing with unseen presences. They may seem harmless but can open back doors that should remain closed.
A sub-type of the "inhuman" haunting is a Poltergeist. Poltergeist aren't considered a spirit or demon and they are more mischievous than malevolent which an adolescent boy or girl is almost always the center of it all. What you expect in a brief episode is floating or flinging of kitchen utensils, thunderous poundings reverberating in walls and ceilings, heavy furniture moved about or tossed by an unseen force, and, on rare occasions, disembodied voices. It usually lasts a few months to a few years and has benn to known to follow a family to a new residence. I guess in these situations its better to ride it out rather than relocating.