Here is what BDB and Thayer have to say about the words that seem to be most often translated as soul and spirit.
Soul
nephesh
BDB Definition:
1) soul, self, life, creature, person, appetite, mind, living being, desire, emotion, passion
1a) that which breathes, the breathing substance or being, soul, the inner being of man
1b) living being
1c) living being (with life in the blood)
1d) the man himself, self, person or individual
1e) seat of the appetites
1f) seat of emotions and passions
1g) activity of mind
1g1) dubious
1h) activity of the will
1h1) dubious
1i) activity of the character
1i1) dubious
Spirit
rûach
BDB Definition:
1) wind, breath, mind, spirit
1a) breath
1b) wind
1b1) of heaven
1b2) quarter (of wind), side
1b3) breath of air
1b4) air, gas
1b5) vain, empty thing
1c) spirit (as that which breathes quickly in animation or agitation)
1c1) spirit, animation, vivacity, vigour
1c2) courage
1c3) temper, anger
1c4) impatience, patience
1c5) spirit, disposition (as troubled, bitter, discontented)
1c6) disposition (of various kinds), unaccountable or uncontrollable impulse
1c7) prophetic spirit
1d) spirit (of the living, breathing being in man and animals)
1d1) as gift, preserved by God, Gods spirit, departing at death, disembodied being
1e) spirit (as seat of emotion)
1e1) desire
1e2) sorrow, trouble
1f) spirit
1f1) as seat or organ of mental acts
1f2) rarely of the will
1f3) as seat especially of moral character
1g) Spirit of God, the third person of the triune God, the Holy Spirit, coequal, coeternal with the Father and the Son
1g1) as inspiring ecstatic state of prophecy
1g2) as impelling prophet to utter instruction or warning
1g3) imparting warlike energy and executive and administrative power
1g4) as endowing men with various gifts
1g5) as energy of life
1g6) as manifest in the Shekinah glory
1g7) never referred to as a depersonalized force
In the Greek the spirit and the soul overlap
Soul
G5590
ψυχή
psuchē
Thayer Definition:
1) breath
1a) the breath of life
1a1) the vital force which animates the body and shows itself in breathing
1a1a) of animals
1a1b) of men
1b) life
1c) that in which there is life
1c1) a living being, a living soul
2) the soul
2a) the seat of the feelings, desires, affections, aversions (our heart, soul etc.)
2b) the (human) soul in so far as it is constituted that by the right use of the aids offered it by God it can attain its highest end and secure eternal blessedness, the soul regarded as a moral being designed for everlasting life
2c) the soul as an essence which differs from the body and is not dissolved by death (distinguished from other parts of the body)
Spirit
pneuma
Thayer Definition:
1) the third person of the triune God, the Holy Spirit, coequal, coeternal with the Father and the Son
1a) sometimes referred to in a way which emphasises his personality and character (the
\\Holy\\ Spirit)
1b) sometimes referred to in a way which emphasises his work and power (the Spirit of
\\Truth\\)
1c) never referred to as a depersonalised force
2) the spirit, i.e. the vital principal by which the body is animated
2a) the rational spirit, the power by which the human being feels, thinks, decides
2b) the soul
3) a spirit, i.e. a simple essence, devoid of all or at least all grosser matter, and possessed of the power of knowing, desiring, deciding, and acting
3a) a life giving spirit
3b) a human soul that has left the body
3c) a spirit higher than man but lower than God, i.e. an angel
3c1) used of demons, or evil spirits, who were conceived as inhabiting the bodies of men
3c2) the spiritual nature of Christ, higher than the highest angels and equal to God, the divine nature of Christ
4) the disposition or influence which fills and governs the soul of any one
4a) the efficient source of any power, affection, emotion, desire, etc.
5) a movement of air (a gentle blast)
5a) of the wind, hence the wind itself
5b) breath of nostrils or mouth