You may wonder if it's possible to move cards between board views. The answer is "yes". When you select several cards, they appear in the clipboard area at the bottom.
If you go to other board views, this clipboard is still visible. You can navigate to another board view, drag cards from the clipboard and drop them:
Note, that with this action you just change some card's properties. It may happen, that card is still visible on previous view and on the new view.