It sounds like your computer thinks you have two monitors, and it is showing you the extended desktop which is usually displayed on the second screen.
Just a guess though.
I've had a possibly similar problem: If I wake the NUC before turning the TV on there will be no signal on the HDMI at all (to clarify, the NUC is attached to the tv using HDMI. there is nothing attached to DP). However, if I turn on the TV first everything will work as expected. If I have no image I can press ctrl+alt+F1 to get a new TTY and restart Xorg to get my desktop back. Rebooting also works ofc. Haven't had time to investigate further.