In X11 terminology.
Display: at least one screen, a keyboard, and a pointing device (often a mouse).
Screen: What everyone else calls a display, monitor, or screen, but could be virtual, e.g. a region of a monitor (window).
Both screens and windows are addressable via the DISPLAY environment variable, and some other means. An application can choose which display.screen to map a window to. But it is not possible to move a window to another screen, without the application un-mapping and re-mapping it.
Monitor: This is (I think), a newer idea. Each screen can be made up of monitors. Generally application don't know about monitors, except the window manager. The window manager can freely move windows between monitors, and even overlap. All monitors are mapped as a single rectangular screen. But the window manager knows where monitors start and end, and can full-screen to just one, or detect monitor edge gestures. (I think a monitor is probably no more that a set of hints that the window manager uses). If your window manager is not monitor aware, then windows will full-screen over the whole screen.
Screens are not used much these days, at least not for interactive desktops, if using a window manager that supports monitors. However screens would be useful, when the application should be in charge, as opposed to the window manager. Though this does not seem to be necessary: Open-office presents, knows of, and uses monitors when presenting.