handwriting vs writing

handwriting and writing both are nouns.

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

As nouns, writing is a hypernym of handwriting; that is, writing is a word with a broader meaning than handwriting:

Other hypernyms of handwriting include committal to writing.

As nouns, writing is a hypernym of handwriting; that is, writing is a word with a broader meaning than handwriting:

handwriting: something written by hand
writing: letters or symbols that are written or imprinted on a surface to represent the sounds or words of a language

handwriting (noun)	writing (noun)
the activity of writing by hand	the activity of putting something in written form
something written by hand	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