IMO, a soul is basically a spirit with a fleshy vessel. We are spirits with physical extensions. You can do anything with the soul that you can do with independent spirits, and you can also separate it from it’s vessel.
According to occultism there are the astral body and the spirit. The first is composed of lower and higher astral; the Hermetism calls those Lunar and Mercurial Body.
Now, man either has an immortal part or probably it wouldn’t be possible to extend immortality like some “doctrines” teach. Some esoteric schools of thought says that after death the astral body reduces itself to a seed or that it doesn’t exist at all (and the mind proceeds to disgregate), but is a sort of task to be realized during spiritual growth.
The soul in Christianity is composed by (supposed or real) astral and spirit. Sometimes the name “soul” is assigned to the spirit, other times to the astral body.