authorship vs writing

authorship and writing both are nouns.

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

As nouns, authorship and writing are synonyms defined as:

Other synonyms of authorship include composition, penning.

authorship (noun)	writing (noun)
the act of creating written works	the activity of putting something in written form
the act of initiating a new idea or theory or writing	the act of creating written works
	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