Take note of the “DISPLAY” variable, this is the local port (on the machine called “desktop”) which is forwarding X11 server commands to the X11 client running on the machine called “laptop”.
user@desktop:~$ vlc &
This sets the “DISPLAY” variable to the first screen on the desktop, and starts VLC as a background process. For this to work you must be logged into the server with the same user account, and have an X11 client running on the desktop.
user@server:~$ gedit &
This sets the “DISPLAY” variable to the laptop, and starts Gedit on the server, but displaying it on the laptop.