As others have pointed out this is more of a philosophical question than a theological one. I’ve personally never seen a clear explaination of what the spirit is supposed to be apart from the soul, but based on some writings (and St. Paul’s writings included) I would guess that it has something to do with the fact that our souls are not merely animating, but connect us with God. While in the West this connection would be defined as an aspect of our soul (hence we can speak of spiritual souls, as opposed to the material souls of plants and animals) it doesn’t amount to a fundamental difference; what is called “spirit” by some Eastern theologians is entirely accounted for by Western theologians, just as “nous”, or heart, is commonly spoken of in the East to refer to a combination of our will, drive, and spiritual connection with God, while the West tends to speak of all of these things under the headings of will and the mind.
If the spirit is viewed as a distinct part of human nature which rises us above the animal (who also have souls), it doesn’t change any of the doctrines of the Faith whatsoever, and is only a factor in how one explains our nature. It’s more akin to the difference between using modern biological/imperical terminology to speak of the body, or classical Aristotelian terminology.
Peace and God bless!
