I too see this inconsistent behaviour. It looks like Apple implemented two strategies: an "old" one which respects the traditional clipboard, and a "new" one which uses small overlay panes in some notional sweetspot and gives you a 3 second (or thereabouts) window of time to drag-and-drop the screenshot.
I don't think they workshopped how they play together, or how a user controls when which one is invoked or what desktop switching to find another context to "paste" into.
Grrrr. No solution, just validating your perception.