cataract surgery vs eye surgery

cataract surgery and eye surgery both are nouns.

Word	Noun	Adjective	Verb	Adverb
cataract surgery	Yes	No	No	No
eye surgery	Yes	No	No	No

As nouns, eye surgery is a hypernym of cataract surgery; that is, eye surgery is a word with a broader meaning than cataract surgery:

cataract surgery: eye surgery that involves removing all or part of the lens and replacing it with an intraocular lens implant
eye surgery: any surgical procedure involving the eyes

Other hypernyms of cataract surgery include eye operation.

cataract surgery (noun)	eye surgery (noun)
eye surgery that involves removing all or part of the lens and replacing it with an intraocular lens implant	any surgical procedure involving the eyes