There are many types of spirit beings in the world, but all have one thing in common - they have no corporeal form. When a spirit achieves corporeal form, it becomes something else entirely - a monster.
Soul Beings vs Spirit Beings
There are two primary classifications of spirit beings: souls that remain after death, and spiritual entities tied to magic and religion. Souls come from living beings which have died, and they have a variety of forms and abilities. Spirits were not attached to a living thing and require some sort of a vessel in order to interact with the world of humans. The distinction may be subtle, but it is vital when determining how to remove an unwanted entity from a location or person.
Spirit, ghost, and soul are often used interchangeably, but specificity can be important for contact/control of the entity.
Ghosts (aka Spirits, Poltergeists, Etc)
There are generally two types of ghosts - echos of souls that reenact moments of their life and active souls interacting with the world. In most cases the benign ghosts, while creepy, fade with time. The echos of souls are the figures seen in windows, or moving through halls, and sometimes they make sounds, but they are repeating things that happened, not engaging in new activities. The active ghosts maintain part of their emotions and consciousness. These are the helpful spiritual guardians and malevolent poltergeists.
Ghosts are often bound to a place or person by the circumstances of their death. The most commonly known ghosts are the ones tied to a location. Less common in western culture, but more common in general, are the benevolent ghosts of ancestors who are tied to a bloodline.
In general ghosts stick around for a reason. If a ghost needs to be removed, the easiest way is to resolve whatever they are trying to achieve. If this goal can not be ascertained through research, a seance can be used to ask them what they need (though this can be risky if the ghost is angry). Alternatively there are rituals which can use magic to push a spirit on to the "other side," wherever that is. In general ghosts are only accessible from beyond the mortal coil for a short time after death, or if there is a strong tie to summon them. For example, bones of the deceased, blood of their living relatives, items belonging to the deceased, etc, are good ways to entice the soul to the world of the living for a chat.
NOTE: Many religions have some sort of spiritual being, but this bit of lore is focused on Christian interpretations of Angels. I, the author, am taking many liberties with the information from the Bible for creative purposes.
So here's the thing about angels - there isn't really very much about them in the Bible. Most of angelic lore comes from extra-biblical traditions, and is largely inaccurate when compared to the source material.
Angels also appear in the Torah (wiki) and the Quran (wiki), but I'm focusing on the Christian texts because that's what I am most familiar with. For fear of going into a deep tangent, I will try to keep this to the relevant information for game.
Angels were created as spirit beings with free will. They were used as messengers for the Christian God. They also appeared in dreams, exacted divine retribution, and generally hung around during the biblical times. In the Bible only two angels appeared on Earth. They were always described as handsome young men, usually dressed in white. Angels were never described as female, and while the biblical authors waxed poetic about the millions of angels in Heaven, only two were named: Michael and Gabriel.
So here is where we diverge from the texts and get creative....
SPOILERS BELOW! Highlight to read.
For our purposes, Angels are Spirit beings, and therefore have no physical form. However, they can possess people. Because Devils are fallen Angels, Devils can do the same. The difference is how the Angel/Devil possess a persons body.
Also, the person's body does not become immortal - it still needs water, food, rest, etc. The Angelic energy helps the flesh heal faster and be stronger, etc, but Angels can not, in and of themselves, create miracles. As messengers of God the angels could bring miracles to humans, but they can not make miracles happen - mostly.
When God could not bring about the prophecies of Revelations (lol, free will) God gave up and fucked off, closing the gates of Heaven. All of the angels and devils who were not in Heaven became trapped on earth. Sine then the Angels and Devils discovered that they can, through their actions, change from Angel to Devil, and vice-versa.
Why would an angel chose to do this? Well, if an Angel becomes too good, they gain physical form as a Cherubim.
If a Devil becomes too evil, they gain physical form as a Demon.
For the most part Cherubim and Demons ascend/descend to Paradise or Sheol, but every now and then they are summoned to Earth...