churchman vs man of the cloth

churchman and man of the cloth both are nouns.

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

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

churchman: a clergyman or other person in religious orders
man of the cloth: a member of the clergy and a spiritual leader of the Christian Church

Other hypernyms of churchman include clergyman, reverend.

churchman (noun)	man of the cloth (noun)
a clergyman or other person in religious orders	a member of the clergy and a spiritual leader of the Christian Church