postulator vs man of the cloth

postulator and man of the cloth both are nouns.

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

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

postulator: (Roman Catholic Church) someone who proposes or pleads for a candidate for beatification or canonization
man of the cloth: a member of the clergy and a spiritual leader of the Christian Church

Other hypernyms of postulator include clergyman, reverend.

postulator (noun)	man of the cloth (noun)
someone who assumes or takes something for granted as the basis of an argument	a member of the clergy and a spiritual leader of the Christian Church
(Roman Catholic Church) someone who proposes or pleads for a candidate for beatification or canonization