Not sure about the stance of the Christian Church. Personally, I believe the spirit is the breath of life given by God to Adam and to all mankind since. Energy, potential, a seed of Consciousness maybe if we argue only humans have a spirit or consciousness. God is Spirit. John 4:24
If I am not mistaken, the word for breath and spirit are interchangeable in the Old Testament, or at least the Genesis account. And this may be why Jewish people don’t consider a child to be a person until the baby takes its first breath outside the womb. Though there seems to be debates on when what occurs.
I believe I once read that the soul, on the other hand, is a culmination or summation of all you are. Body, heart, mind, will, spirit. Without any one of these parts, you are dead and cease to be. The spirit component returns to God and/or whatever else is left of you, called a Shade, goes to the place of the dead.
One would wonder, if the Christian Theology is not cohesive with Judaism in some of these fundamental points, does it really share roots with that faith?