The problem is that mapping has many definitions, and I am realizing now that I was thinking of it in cartographic terms. To me, the dilemma arises when mapping is intrinsically associated with an expression, which is when it begins to conceptually overlap with visualization. With that in mind, I was approaching the distinction between both terms at the level of the generic/superordinate (visualization) and the specific/subordinate (mapping).

That said, I actually find your argumentation much clearer. It helps to think of the relationship between the two terms as conceptual process vs. expression. (Though I don’t quite agree with your comment on agency—I think it plays an important role precisely in the conceptual process, as the metaphoric “bridge” between two worlds. Any expression, of course, as you rightly point out, is equally subjective. But I would argue that agency begins with the cognitive model).