I received a Personal Message using this system from JT. I replied to it. Then, I wanted to save it. I had no appropriate Folder, so I created a Folder and named it "Saved". I then selected "Saved" below the message, checked the checkbox to the right of the message, and clicked the "move to" button. Sure enough, a copy of the message was placed in my "Saved" Folder. However, the original was still in my Inbox. Once I deleted the original, the copy was still in my "Saved" folder.
Therefore, I must assume that "move to" really means "copy to" in the Personal Message context. Please either fix the functionality or rename the button.