speechwriter vs writer

speechwriter and writer both are nouns.

Word	Noun	Adjective	Verb	Adverb
speechwriter	Yes	No	No	No
writer	Yes	No	No	No

As nouns, writer is a hypernym of speechwriter; that is, writer is a word with a broader meaning than speechwriter:

speechwriter: a writer who composes speeches for others to deliver
writer: writes (books or stories or articles or the like) professionally (for pay)

Other hypernyms of speechwriter include author.

speechwriter (noun)	writer (noun)
a writer who composes speeches for others to deliver	writes (books or stories or articles or the like) professionally (for pay)
	a person who is able to write and has written something