harm vs ill health

harm and ill health both are nouns.

Word	Noun	Adjective	Verb	Adverb
harm	Yes	No	Yes	No
ill health	Yes	No	No	No

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

harm: any physical damage to the body caused by violence or accident or fracture etc.; the condition of an injury
ill health: a state in which you are unable to function normally and without pain

Other hypernyms of harm include health problem, unhealthiness.

harm (noun)	ill health (noun)
the act of damaging something or someone	a state in which you are unable to function normally and without pain
the occurrence of a change for the worse
any physical damage to the body caused by violence or accident or fracture etc.; the condition of an injury

harm (verb)	ill health (verb)
cause or do harm to