Helo papawoody61,
Being able to view your applications on your external display is very important, and the communities is a great place for help to ensure your applications and displays are working as expected. To clarify upon the Desktop images you're asking about are these files, folders, and documents that you have saved to your desktop? If so, are they still showing on your Macs display? If so, this is expected if you have the external display set to as an Extended Desktop. If you're wanting your files, folders, and documents to appear on the external display as well you can mirror your Macs display. This would show the same exact information on both displays, including the apps you have open.
More information about using an external display can be found in the following article.
Use external monitors with your Mac
If you're having an issue where apps that you previously had open aren't showing on the external display please check the dock to make sure the apps aren't minimized. If the apps aren't minimized they may be open in a different desktop using Mission Control. This feature allows you to have multiple Desktops available on one display. While they won't show at the same time, you would be able to scroll through the different Desktops. Information on how to use Missing Control can be found in the following article.
Use Mission Control on your Mac
If you're having a different issue please let us know in more detail about what's going on.
Have a great day.