archdeacon vs man of the cloth

archdeacon and man of the cloth both are nouns.

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

As nouns, man of the cloth is a hypernym of archdeacon; that is, man of the cloth is a word with a broader meaning than archdeacon:

archdeacon: (Anglican Church) an ecclesiastical dignitary usually ranking just below a bishop
man of the cloth: a member of the clergy and a spiritual leader of the Christian Church

Other hypernyms of archdeacon include clergyman, reverend.

archdeacon (noun)	man of the cloth (noun)
(Anglican Church) an ecclesiastical dignitary usually ranking just below a bishop	a member of the clergy and a spiritual leader of the Christian Church