Well. If you were to consider that a poet's tools of the trade
are words and concepts and ideas... then yes, a poet is a writer, a
craftsman that builds and creates through language to convey an
emotion, an observation, an abstract.
Think of the techniques a poet uses in his work: rhythm,
alliteration, repetition, imagery, allusion, bathos, satire,
hyperbole -- these are essential skills that an apt writer must
possess in order to write a good piece of ... something.
And vice versa.
So yes, a poet is a writer who uses words to great effect, who uses
a structural paupacity to fill in, ably, the gaps of
meaning.