writing vs patrology

writing and patrology both are nouns.

Word	Noun	Adjective	Verb	Adverb
writing	Yes	No	No	No
patrology	Yes	No	No	No

As nouns, patrology is a hyponym of writing; that is, patrology is a word with a more specific, narrower meaning than writing:

Other hyponyms of writing include patristics.

writing (noun)	patrology (noun)
the activity of putting something in written form	the study of the lives, writings, and doctrines of the Church Fathers
the act of creating written works	the writings of the early Church Fathers
the work of a writer; anything expressed in letters of the alphabet (especially when considered from the point of view of style and effect)
letters or symbols that are written or imprinted on a surface to represent the sounds or words of a language
(usually plural) the collected work of an author