autograph vs piece of writing

autograph and piece of writing both are nouns.

Word	Noun	Adjective	Verb	Adverb
autograph	Yes	No	Yes	No
piece of writing	Yes	No	No	No

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

autograph: something written by one's own hand
piece of writing: the work of a writer; anything expressed in letters of the alphabet (especially when considered from the point of view of style and effect)

Other hypernyms of autograph include writing, written material.

autograph (noun)	piece of writing (noun)
something written by one's own hand	the work of a writer; anything expressed in letters of the alphabet (especially when considered from the point of view of style and effect)
a person's own signature

autograph (verb)	piece of writing (verb)
mark with one's signature