hospital vs health facility

hospital and health facility both are nouns.

Word	Noun	Adjective	Verb	Adverb
hospital	Yes	No	No	No
health facility	Yes	No	No	No

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

Other hypernyms of hospital include healthcare facility, medical building.

hospital (noun)	health facility (noun)
a health facility where patients receive treatment	building where medicine is practiced
a medical institution where sick or injured people are given medical or surgical care