foundling hospital vs infirmary

foundling hospital and infirmary both are nouns.

Word	Noun	Adjective	Verb	Adverb
foundling hospital	Yes	No	No	No
infirmary	Yes	No	No	No

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

foundling hospital: a hospital where foundlings (infant children of unknown parents) are taken in and cared for
infirmary: a health facility where patients receive treatment

Other hypernyms of foundling hospital include hospital.

foundling hospital (noun)	infirmary (noun)
a hospital where foundlings (infant children of unknown parents) are taken in and cared for	a health facility where patients receive treatment