Different desktop background on different monitors or different virtual screens (virtual desktops, dual monitors, screen saver)

Two things to know:

• Background wallpaper for a second, etc., monitor is not controlled through the main preferences window; a specialized additional preferences window must be opened for the additional monitor. The "System Preferences > Desktop & Screen Saver" window can open a subordinate window, provided you have two monitors. To force this, click between tabs, from "Desktop" to "Screen Saver" and back to "Desktop" again. At this point, an new window should be visible, labeled "Secondary Desktop". This window is subordinate; it cannot be individually minimized or closed as it follows the lead of the "Desktop & Screen Saver" window.
• Previously existing virtual screens do not respond automatically to a change in "Desktop & Screen Saver". On the other hand, a newly created virtual screen will behave as expected, i.e., a newly created virtual screen will have the background wallpaper associated with its monitor (primary vs secondary). The background wallpaper on previously existing screens can be changed one at a time, using "Desktop & Screen Saver" individually for each virtual screen. (Or, just destroy them and create new ones).