I wonder if the real key to origin of Newman’s use of “notion” and “thing” in the Grammar is to be found in the Second Discourse of the Idea, namely in his discussion of the relation of individual sciences to the body of knowledge as a whole. Each science, considered singly, is abstractive and schematizing, and so distorts the objects it considers — only the aspiration to comprehension brings the concrete into view. All very similar to the distinctions operative in the Grammar.
See esp. Idea 3.6