The corners of the diagram might also correspond to goals we seek: exploratory visualization favors efficiency to enable discovery; explanatory visualization needs to be understandable; experiential visualization elicits curiosity joy, worry, or outrage, which may lead to action:
None of this is very original. For instance, these days I'm re-reading Donald A. Norman's classic The Design of Everyday Things, and in its first pages there's this quote: “The major areas of design relevant to this book are industrial design, interaction design, and experience design. None of the fields is well defined, but the focus of the efforts does vary, with industrial designers emphasizing form and material, interactive designers emphasizing understandability and usability, and experience designers emphasizing the emotional impact.”
Also, Andy Kirk's Data Visualisation: A Handbook for Data Driven Design—I recently received its excellent second edition—lists three modes of experience when engaging with a visualization: explanatory, exhibitory, exploratory. Don't miss it: