This is a failure of Windows's screenshot tool though, in my opinion. I find this incredibly clunky. On Plasma/KDE, pressing "print screen" takes a screenshot of the complete screen, and a dialog opens and offers you to copy the screenshot into the clipboard, to save it in a file or to open / edit it with the tool of your choice. You can also take another screenshot of the entire screen, or a window, or an area that you can draw with the mouse, with a delay or not.
On other environments, the screenshot is automatically saved in a file without interaction. I'm not a huge fan but this is what you end up doing most of the time on Windows anyway, but by manually pasting in Paint and saving.