writing style vs poetry

writing style and poetry both are nouns.

Word	Noun	Adjective	Verb	Adverb
writing style	Yes	No	No	No
poetry	Yes	No	No	No

As nouns, poetry is a hyponym of writing style; that is, poetry is a word with a more specific, narrower meaning than writing style:

Other hyponyms of writing style include drama, prose, form, poesy, verse, satire, steampunk.

writing style (noun)	poetry (noun)
a style of expressing yourself in writing	literature in metrical form
	any communication resembling poetry in beauty or the evocation of feeling