specialist vs expert

specialist and expert both are nouns.

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

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

specialist: an expert who is devoted to one occupation or branch of learning
expert: a person with special knowledge or ability who performs skillfully

specialist (noun)	expert (noun)
an expert who is devoted to one occupation or branch of learning	a person with special knowledge or ability who performs skillfully
practices one branch of medicine

specialist (adjective)	expert (adjective)
	having or showing knowledge and skill and aptitude
	of or relating to or requiring special knowledge to be understood