intellect vs mental faculty

intellect and mental faculty both are nouns.

Word	Noun	Adjective	Verb	Adverb
intellect	Yes	No	No	No
mental faculty	Yes	No	No	No

As nouns, mental faculty is a hypernym of intellect; that is, mental faculty is a word with a broader meaning than intellect:

intellect: the capacity for rational thought or inference or discrimination
mental faculty: one of the inherent cognitive or perceptual powers of the mind

Other hypernyms of intellect include faculty, module.

intellect (noun)	mental faculty (noun)
the capacity for rational thought or inference or discrimination	one of the inherent cognitive or perceptual powers of the mind
knowledge and intellectual ability
a person who uses the mind creatively