hospital vs infirmary

hospital and infirmary both are nouns.

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

As nouns, hospital and infirmary are synonyms defined as:

hospital and infirmary: a health facility where patients receive treatment

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