If you save files to the desktop, or to folders on the desktop, it will take up space on whichever drive the OS is installed on unless there is only a shortcut on the desktop that points to a folder located on another drive. The desktop itself is part of the C:/ drive so whichever drive you have the OS installed on, is the desktop.
You can designate downloads to be directed to any folder you want on any drive. Just go into your browsers settings and specify where you want to save them.