mental illness vs mental state

mental illness and mental state both are nouns.

Word	Noun	Adjective	Verb	Adverb
mental illness	Yes	No	No	No
mental state	Yes	No	No	No

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

mental illness: any disease of the mind; the psychological state of someone who has emotional or behavioral problems serious enough to require psychiatric intervention
mental state: (psychology) a mental condition in which the qualities of a state are relatively constant even though the state itself may be dynamic

Other hypernyms of mental illness include mental condition, psychological condition, psychological state.

mental illness (noun)	mental state (noun)
any disease of the mind; the psychological state of someone who has emotional or behavioral problems serious enough to require psychiatric intervention	(psychology) a mental condition in which the qualities of a state are relatively constant even though the state itself may be dynamic