Now that a most basic history of Souls in the Christian Church has been sketched, the words themselves can be handled. The terms spirit and soul in Greek also encompass words for wind and the life or life force itself. This means there is a large scale of meaning that we unfortunately often lose in translation.
The Greek Soul is an old one
According to Ernes De Witt Burton in his book Spirit, Soul, and Flesh (an oldy goldy) the term Ψυχή (Pys-su-kay) is of the oldest antiquity while Πνεύμα (pneuma) first appears in Greek literature circa the 6th and 5th centuries. 
The words Speak to different things
In simplest terms a Πνεύμα is the word of choice for soul-stuff, or an ethereal something, while Ψυχή is the word for life-force and mind-force, (a good way to remember this distinction is the common idea of “psychic powers).
Per Burton the most linguistically challenging and confusing occurrences of the words are when they appear to be used synonymously. Burton claims we must actually deny the initial impression that the terms are interchangeable, and realize that such word use is intended to claim that the functional aspects of the soul are comprised (or result from) of a Πνεύμα substance.
Spirit is more than “just Spirit”
The driving definition of the term pneuma in Ancient Greek is a “wind or gust.” (Think of Jesus’s dialogue in John).
Per Burton’s many examples, many ancient writers referenced even the breath of animals or humans with no deeper philosophical intention than describing inhaled air.
At the same time, there were other writers who did define the term as “a breath of life” or a “divine odor” (a gods presence sensed by olfactory perceptions, like holy incense).
Still, these spiritual meanings are still intended to retain a sense of gusty wind. Burton does note that when metaphysical meanings are attached, the allegorical terms coinciding with these uses still refer to related terms of air or aspiration. Again, this theme is recurring because the metaphysical characteristics ascribed to pneuma from the 5th c B.C. onward carry over this wind meaning.
The Soul of the Matter
Homer envisions Ψυχή of individuals maintaining a separate existence after the physical death of the body. Most interesting is that the polar nature of Greek metaphysical debates appears to have impacted the ranges of meaning to the term Ψυχή far less than Πνεύμα.
Burton claims that we can be fairly confident in claiming that for most Greeks Ψυχή referred to a life-force that when lost resulted in death. Also common was the notion that Ψυχή was the soul, the seat of emotions and reason. As such it was both the aspect of a person that drove moral decisions and failures and the aspect of a person that granted the corpse locomotion.
These two aspects, that the modern mind often separates, are united in the Greek term Ψυχή, lending the term a more holistic sense then the English “soul.”
The terms are both inherently loser than we use think them to be
Certain reflections within Burton’s work need to be repeated here so that the full depth of the terms is appreciated.
While Ψυχή seems to entail an immortal soul, Herodotus actually describes the idea of the immortal soul to an Egyptian origin. While Herodotus is not in the best position to make such claims, Burton relates that all through the classical period up through Aristotle there is certain agnosticism in Greek philosophy regarding the future of the soul.
Additionally, the term Ψυχή can be pulled towards a completely different context then either life-force or a metaphysical construct.
And because Πνεύμα can simply mean “a wind” there is great everyday flexibility under both terms. What is thematic under the exploration of both terms is that striping the everyday meaning and retaining only the purely spiritual and metaphysical aspects does violence even to the spiritual conceptions of the words.
 Ernest De Witt Burton. Spirit, Soul, and Flesh: the usage of pnuema, psyche, and sarx in Greek writings and translated works from the earliest period to 225 A.D., and of their equivalents…in the Hebrew Old Testament. (Chicago: University of Chicago Press, 1918), pp13.