eye operation vs surgery

eye operation and surgery both are nouns.

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

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

eye operation: any surgical procedure involving the eyes
surgery: a medical procedure involving an incision with instruments; performed to repair damage or arrest disease in a living body

Other hypernyms of eye operation include operation, surgical operation, surgical procedure, surgical process.

eye operation (noun)	surgery (noun)
any surgical procedure involving the eyes	a medical procedure involving an incision with instruments; performed to repair damage or arrest disease in a living body
	a room in a hospital equipped for the performance of surgical operations
	a room where a doctor or dentist can be consulted
	the branch of medical science that treats disease or injury by operative procedures