priest vs clergyman

priest and clergyman both are nouns.

Word	Noun	Adjective	Verb	Adverb
priest	Yes	No	No	No
clergyman	Yes	No	No	No

As nouns, clergyman is a hypernym of priest; that is, clergyman is a word with a broader meaning than priest:

priest: a clergyman in Christian churches who has the authority to perform or administer various religious rites; one of the Holy Orders
clergyman: a member of the clergy and a spiritual leader of the Christian Church

Other hypernyms of priest include man of the cloth, reverend, Holy Order, Order.

priest (noun)	clergyman (noun)
a clergyman in Christian churches who has the authority to perform or administer various religious rites; one of the Holy Orders	a member of the clergy and a spiritual leader of the Christian Church
a person who performs religious duties and ceremonies in a non-Christian religion