$DISPLAY is definitely different for each X11 screen, ie. :0.0 for the first screen, :0.1 for the second and so on. (:1, :2 is used for more instances of the X11 server).

I can't recall any application able to use multiple X11 screens (except in the trivial sense that you could set DISPLAY when starting the application), and I've been using X11 since X11R4.