subconscious mind vs psyche

subconscious mind and psyche both are nouns.

Word	Noun	Adjective	Verb	Adverb
subconscious mind	Yes	No	No	No
psyche	Yes	No	No	No

As nouns, psyche is a hypernym of subconscious mind; that is, psyche is a word with a broader meaning than subconscious mind:

subconscious mind: psychic activity just below the level of awareness
psyche: that which is responsible for one's thoughts, feelings, and conscious brain functions; the seat of the faculty of reason

Other hypernyms of subconscious mind include brain, head, mind, nous.

subconscious mind (noun)	psyche (noun)
psychic activity just below the level of awareness	that which is responsible for one's thoughts, feelings, and conscious brain functions; the seat of the faculty of reason
	the immaterial part of a person; the actuating cause of an individual life