I think the answer to your question comes from within the piece itself: this is a thoughtful and philosophical sort of poem whereas so much of what you write is emotive, so certainly poets are writers too.
Are writers poets? Not necessarily from a technical point, I suppose, but all the best writers - be them poets or not - write with feeling and thought. That's my opinion, anyhow.
Sir Ben was right. He said it already.Poet is synonymous of a writer or an author. Poet can be called author or writer as well but a writer of a book or an article Can not be called a poet. ..Ahh you got me too.lol