ophthalmologist vs specialist

ophthalmologist and specialist both are nouns.

Word	Noun	Adjective	Verb	Adverb
ophthalmologist	Yes	No	No	No
specialist	Yes	No	No	No

As nouns, specialist is a hypernym of ophthalmologist; that is, specialist is a word with a broader meaning than ophthalmologist:

ophthalmologist: a medical doctor specializing in the diagnosis and treatment of diseases of the eye
specialist: practices one branch of medicine

Other hypernyms of ophthalmologist include medical specialist.

ophthalmologist (noun)	specialist (noun)
a medical doctor specializing in the diagnosis and treatment of diseases of the eye	an expert who is devoted to one occupation or branch of learning
	practices one branch of medicine