ill health vs harm

ill health and harm both are nouns.

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

As nouns, harm is a hyponym of ill health; that is, harm is a word with a more specific, narrower meaning than ill health:

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

ill health (noun)	harm (noun)
a state in which you are unable to function normally and without pain	the act of damaging something or someone
	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

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