Ghosts, spectres, wraiths and spirits are physical or visual manifestations of (stray) souls, either being made out of ectoplasm (so they can interract with the physical world), or being completely immaterial and incapable of interacting with the physical world, save for visually appearing to individuals and communicating with them.
The term "spirit" implies the latter of the two, as well as either good intent, or association with an abstract concept or an idea. The terms "wraith" and "spectre" imply the earlier, as well as malintent and association with necromancy. The term "ghost" is considered neutral and can be used to mean both.
Spirits are not made out of ectoplasm, and in fact have no real physical substance at all - they are instead comparable to an astral projection. As such, they are incapable of physically interacting with the world, save for making themselves seen and heard.
Spirits can appear in various ways, most of them consensually - spirits of past heroes can be summoned (provided that their souls aren't occupying any currently living bodies, because of reincarnation) to guide the people in the present, some highly influential people (such as saints) simply do not reincarnate but instead become spirits, eternally guiding followers of an idea or religion.
Unlike wraiths, spirits cannot possess bodies without the person's consent, and even in that scenario, "possessing" spirits usually instead provide aid rather than ful control.
Wraiths and Spectres
Wraiths and spectres are products of necromancy, albeit a special form of it: rather than breathing physical life into a lifeless physical body without injecting it with a soul, wraiths and spectres are created by trapping and enslaving the souls of those who had unfinished business on this world before their untimely demise, especially (but not limited to) vengeful individuals. After the entrapment, a contract may be optionally made, where the necromancer may be forced to either release the ghost or grant the ghost a wish (usually injecting the soul into an intact body) after the ghost completes a certain objective - however, this is entirely optional, and indefinite enslavement of a ghost is not unheard of either.
Wraiths and spectres have their physical bodies constructed out of ectoplasm, a gooey, semi-transparent material that will leak through even some of the most dense materials, allowing wraiths and spectres to fly through walls. This gives them a resistance (but not immunity) towards both particles and kinetic energy, but they have a weakness towards fire and thunder. Pure magical energy is also known to be the wraith-bane.
Wraiths and spectres are known for temporarily possessing the bodies of weak-minded individuals. When a wraith enters a mutually beneficial contract with a necromancer rather than being outright enslaved, a common request is to be provided with a body that resembled their own that they can possess until they can finally live the life that they interrupted.
The strength of these ghosts depends on two factors: how strong the necromancer has made them, and how unwilling they are to give up on their interrupted existence on this world. A ghost that is determined that he/she had more to live for and just cannot let go will be much more difficult to kill than one that is willing to let go. In fact, a wraith or spectre can also be killed by just convincing them to let go: a ghost that "lets go" just breaks the connection between their soul and the ectoplasm, effectively commiting suicide. Necromancers on the other have measures against this - they commonly invoke vivid images of whatever made these souls vengeful in the first place. A common punishment for spectres that fail missions is invoking vivid imagery of their worst fears.