From Strong's:
nephesh:
Definition
a soul, living being, life, self, person, desire, passion, appetite, emotion
NASB Word Usage
any (1), anyone (2), anyone* (1), appetite (7), being (1), beings (3), body (1), breath (1), corpse (2), creature (6), creatures (3), dead (1), dead person (2), deadly (1), death (1), defenseless* (1), desire (12), desire* (2), discontented* (1), endure* (1), feelings (1), fierce* (2), greedy* (1), heart (5), heart's (2), herself (12), Himself (4), himself (19), human (1), human being (1), hunger (1), life (146), life* (1), lifeblood* (2), lives (34), living creature (1), longing* (1), man (4), man's (1), men* (2), mind (2), Myself (3), myself (2), number (1), ones (1), others (1), ourselves (3), own (1), passion* (1), people (2), people* (1), perfume* (1), person (68), person* (1), persons (19), slave (1), some (1), soul (238), soul's (1), souls (12), strength (1), themselves (6), thirst (1), throat (2), will (1), wish (1), wishes (1), yourself (11), yourselves (13).
and
ruach:
Definition
breath, wind, spirit
NASB Word Usage
air (2), anger (1), blast (2), breath (31), breathless* (1), cool (1), courage (1), despondency* (1), exposed (1), grief* (1), heart (1), inspired (1), mind (3), motives (1), points (1), quick-tempered* (1), side (4), sides (2), Spirit (76), spirit (127), spirits (3), strength (1), temper (2), thoughts* (1), trustworthy* (1), wind (98), winds (7), windy (2), wrath (1).
For a passage that uses both words:
Eze 18:20 The soul (nephesh) who sins is the one who will die. The son will not share the guilt of the father, nor will the father share the guilt of the son. The righteousness of the righteous man will be credited to him, and the wickedness of the wicked will be charged against him.
Eze 18:21 "But if a wicked man turns away from all the sins he has committed and keeps all my decrees and does what is just and right, he will surely live; he will not die.
....
Eze 18:31 Rid yourselves of all the offenses you have committed, and get a new heart and a new spirit (ruach). Why will you die, O house of Israel?
So clearly this is suggesting that a soul might not die and that a spirit is something that will die and will need to be renewed. Which is quite the opposite of what you are suggesting.
Psyche and spirit both come from words that can mean "breath" and I also note that Strongs says of nephesh "From naphash; properly, a breathing creature". In Genesis 2:7 God breathes into the nostrils of the man he has formed and the man becomes a nephesh.
So I think the words are closer than you think and also each can mean a number of things.
It is probably a mistake to assume that the usage of these words in the Bible was any more precise or less ambiguous than the usage of the equivalent words we have in our language today.