unfitness vs health problem

unfitness and health problem both are nouns.

Word	Noun	Adjective	Verb	Adverb
unfitness	Yes	No	No	No
health problem	Yes	No	No	No

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

unfitness: poor physical condition; being out of shape or out of condition (as from a life of ease and luxury)
health problem: a state in which you are unable to function normally and without pain

Other hypernyms of unfitness include ill health, unhealthiness.

unfitness (noun)	health problem (noun)
the quality of not being suitable	a state in which you are unable to function normally and without pain
lacking the power to perform
poor physical condition; being out of shape or out of condition (as from a life of ease and luxury)