dropping the show removes it from your up next but keeps the progress visible. hiding a show removes the progress altogether so someone browsing your history wont even see the hidden show (although the watch times are still counted in your overall watch times)
Drop hides it from up next, progress, and calendar with one action. If you watch an episode of a dropped show, it is automatically restored and undropped.
Drop also removes it from your progress. I plan on adding an option to view the dropped shows on the progress page though.