writing style vs poesy

writing style and poesy both are nouns.

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

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

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

writing style (noun)	poesy (noun)
a style of expressing yourself in writing	literature in metrical form