This is a pretty general question which comes down to a question about the differences between philosophy and psychology more broadly. In general, psychology emphasizes questions that can be resolved empirically (i.e. by observation), while philosophy emphasizes questions which can't.
That said, philosophy and psychology of art have influenced each other tremendously. Many early-modern and modern English-speaking philosophers of art made claims that might be considered psychological (Hume, Burke, Kant). You have already noticed some of the influence between the fields in both directions. It is significant, and characterizing all the kinds of influence would take a much longer answer. I would just keep an eye open for overlaps in the current work like Walton's you're reading now.