pathology vs health problem

pathology and health problem both are nouns.

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

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

pathology: any deviation from a healthy or normal condition
health problem: a state in which you are unable to function normally and without pain

Other hypernyms of pathology include ill health, unhealthiness.

pathology (noun)	health problem (noun)
the branch of medical science that studies the causes and nature and effects of diseases	a state in which you are unable to function normally and without pain
any deviation from a healthy or normal condition