Father vs Church Father

Father and Church Father both are nouns.

Word	Noun	Adjective	Verb	Adverb
Father	Yes	No	No	No
Church Father	Yes	No	No	No

As nouns, Father and Church Father are synonyms defined as:

Father and Church Father: (Christianity) any of about 70 theologians in the period from the 2nd to the 7th century whose writing established and confirmed official church doctrine; in the Roman Catholic Church some were later declared saints and became Doctor of the Church; the best known Latin Church Fathers are Ambrose, Augustine, Gregory the Great, and Jerome; those who wrote in Greek include Athanasius, Basil, Gregory Nazianzen, and John Chrysostom

Other synonyms of Father include Father of the Church.

Father (noun)	Church Father (noun)
`Father' is a term of address for priests in some churches (especially the Roman Catholic Church or the Orthodox Catholic Church); `Padre' is frequently used in the military	(Christianity) any of about 70 theologians in the period from the 2nd to the 7th century whose writing established and confirmed official church doctrine; in the Roman Catholic Church some were later declared saints and became Doctor of the Church; the best known Latin Church Fathers are Ambrose, Augustine, Gregory the Great, and Jerome; those who wrote in Greek include Athanasius, Basil, Gregory Nazianzen, and John Chrysostom
God when considered as the first person in the Trinity
(Christianity) any of about 70 theologians in the period from the 2nd to the 7th century whose writing established and confirmed official church doctrine; in the Roman Catholic Church some were later declared saints and became Doctor of the Church; the best known Latin Church Fathers are Ambrose, Augustine, Gregory the Great, and Jerome; those who wrote in Greek include Athanasius, Basil, Gregory Nazianzen, and John Chrysostom