clinic vs health facility

clinic and health facility both are nouns.

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

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

Other hypernyms of clinic include healthcare facility, medical building.

clinic (noun)	health facility (noun)
a healthcare facility for outpatient care	building where medicine is practiced
meeting for diagnosis of problems and instruction or remedial work in a particular activity
a medical establishment run by a group of medical specialists