You can configure different actions for drag & drop with the Left/Middle mouse buttons (as a single event), as well as when Ctrl, Shift or Alt are held down. And also (separate) actions for double-click with Left and Middle buttons.
Drag & drop with the Right mouse button will (almost*) always open a (configurable) menu of further choices. (*You can change what the right button does in Power Mode, but you're probably better off using the Left and Middle buttons if you want copy and move on separate mouse buttons.)
By the way, Amorax's answer was about toolbar buttons (like "Copy Files", "Move" and "Rename" on the default toolbars) being able to have separate left, right and middle-click actions. You can copy and move things via toolbar buttons as well, but what he linked to does not apply to drag & drop. The FileTypes area, which you've found, is the right place to look for configuring drag & drop actions.