When connecting my MacBook pro 13 to a projector or monitor only my wallpaper appears, no desktop or video. How do I fix this?

Welcome to the Apple Support Communities.

You need to mirror your display. Go to System Preferences > Displays to adjust the settings.

Jack

You are in extended display mode. Either drag windows to the external display or do as Jack-19 suggested.

In order for a Mac display to become active, your Mac queries the displays, and the display responds with its NAME and capabilities.

The arrangement pane will come up in a window named for the display you have connected. There is no need to type this name, because the display itself provides it.

The examples I posted are for different Macs with different displays connected. The first is for a display that self-reports as "'ThunderBolt display". The second is for a display that self reports as "Built-in retina Display". The ARRANGEMENT sub-pane is what is shown.

System preferences > Displays will come up in a window with the name of your current display.

This is what NOT mirrored will show you:

For contrast, this is Mirrored:

Note that in Mirrored, the two displays' Icons almost completely overlap. There is just enough space to select one and drag it to a different position in space, if that is your preference..