anaesthetist vs specialist

anaesthetist and specialist both are nouns.

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

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

anaesthetist: a specialist who administers an anesthetic to a patient before he is treated
specialist: practices one branch of medicine

Other hypernyms of anaesthetist include medical specialist.

anaesthetist (noun)	specialist (noun)
a specialist who administers an anesthetic to a patient before he is treated	an expert who is devoted to one occupation or branch of learning
	practices one branch of medicine