composer vs songwriter

composer and songwriter both are nouns.

Word	Noun	Adjective	Verb	Adverb
composer	Yes	No	No	No
songwriter	Yes	No	No	No

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

Other hyponyms of composer include contrapuntist, psalmist, ballad maker, songster, symphonist.

composer (noun)	songwriter (noun)
someone who composes music, usually as a profession	a composer of words or music for popular songs