priest vs man of the cloth

priest and man of the cloth both are nouns.

Word	Noun	Adjective	Verb	Adverb
priest	Yes	No	No	No
man of the cloth	Yes	No	No	No

As nouns, man of the cloth is a hypernym of priest; that is, man of the cloth 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
man of the cloth: a member of the clergy and a spiritual leader of the Christian Church

Other hypernyms of priest include clergyman, reverend, Holy Order, Order.

priest (noun)	man of the cloth (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