sanity vs mental health

sanity and mental health both are nouns.

Word	Noun	Adjective	Verb	Adverb
sanity	Yes	No	No	No
mental health	Yes	No	No	No

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

sanity: normal or sound powers of mind
mental health: the psychological state of someone who is functioning at a satisfactory level of emotional and behavioral adjustment

sanity (noun)	mental health (noun)
normal or sound powers of mind	the psychological state of someone who is functioning at a satisfactory level of emotional and behavioral adjustment