Catholic Pope vs Holy Father

Catholic Pope and Holy Father both are nouns.

Word	Noun	Adjective	Verb	Adverb
Catholic Pope	Yes	No	No	No
Holy Father	Yes	No	No	No

As nouns, Catholic Pope and Holy Father are synonyms defined as:

Other synonyms of Catholic Pope include Bishop of Rome, pontiff, pope, Roman Catholic Pope, Vicar of Christ.

Catholic Pope (noun)	Holy Father (noun)
the head of the Roman Catholic Church	the head of the Roman Catholic Church