They seem very similar to me, but I judge that they were given two distinct Wikipedia pages for a reason. Is the difference that a "first principle" is a predicated statement while a "primitive notion" can only serve as the subject of such a statement? The Wikipedia page for primitive notion states that a primitive notion "...is analogous to an axiom", so hence can be predicated, but the content of the rest of the page seems to contradict this. Perhaps "primitive notion" is a more general type than "first principle"?
Primitive notions are undefined concepts within a theory. For example, a theory of meaning may have causation as a primitive notion. A theory of causation, obviously, will not.
First principles are propositions that are not argued for in a theory -- maybe because they are considered self-evident. For example that we know our Ideas and Impressions, in Hume's philosophy; that (Descartes) thinks, in Descartes's philosophy.
So, a primitive notion is expressed by a noun phrase: "causation", "the good". First principles are expressed by sentences: "I think", "We know our Ideas and Impressions".