ego vs psyche

ego and psyche both are nouns.

Word	Noun	Adjective	Verb	Adverb
ego	Yes	No	No	No
psyche	Yes	No	No	No

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

ego: (psychoanalysis) the conscious mind
psyche: that which is responsible for one's thoughts, feelings, and conscious brain functions; the seat of the faculty of reason

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

ego (noun)	psyche (noun)
(psychoanalysis) the conscious mind	that which is responsible for one's thoughts, feelings, and conscious brain functions; the seat of the faculty of reason
your consciousness of your own identity	the immaterial part of a person; the actuating cause of an individual life
an inflated feeling of pride in your superiority to others