Is naturalism art the same as Impressionism?

Far from it. Naturalism in arts is not exactly a movement, but rather a trend within Realism, concerned mostly with the depiction of landscapes voided of the ideosyncrasies of Romanticism. It became the prime subject for artists like Millet and Corot and led them to found the Barbizon School.

However naturalism (uncapitalized) should be understood first of all as a form of methodological observation of nature wich preceeds Realism in Arts. Examples of naturalist paintings with no artistic aspirations would be the illustrations of Charles Darwin, or the botanical drawings in an illustrated encyclopedia.