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A display server or window server is a program whose primary task is to coordinate the input and output of its clients to and from the rest of the operating system, the hardware, and each other. The display server communicates with its clients over the display server protocol, a communications protocol, which can be network transparent or simply network capable.
Available display server communications protocols
One example of a display server is the X.Org Server, which runs on top of the kernel. It receives data from evdev and passes it to one of its clients. The display server also receives data from its clients; it processes the data, it does the compositing and passes the data to one of three kernel components – DRM, or KMS driver. The component writes the data into the framebuffer and content of the framebuffer is transmitted to the connected screen and displayed. X relies on GLX.
One of the implementations of display server concept is X Window System, in particular its actually used version – X.Org Server and Xlib and XCB client libraries. The X.Org Server is a display server, but in its current implementation it relies on a second program, the compositing window manager, to do the compositing. Examples are Mutter or KWin.
Notable examples of display servers implementing the X11 display server protocol are X.Org Server, XFree86, X11.app and Cygwin/X, while client libraries implementing the X11 display server protocol are Xlib and XCB.
One tool called xev is a unix command which creates a window and then asks the display server to send information of events every time something happens to the window (like if it's resized, if any keys are pushed, if it's clicked it etc.) to the console.
Display servers that implement the Wayland display server protocol, are called Wayland compositors. Like any display server, a Wayland compositor is responsible for handling input and output for its clients and – in contrast to X11 – additionally for the compositing. Examples are Weston, Mutter, KWin or Enlightenment.
Wayland compositors communicate with wayland clients over the Wayland display server protocol. This protocol defines that clients can directly write data into the framebuffer using the EGL rendering API. The display server still gets to decide which window is on top and thus visible to the user and also still is responsible for passing data regarding to input devices from evdev to its clients.
The Mir display server comes with its own Mir display server protocol different from the protocols X11 or Wayland! Mir shall additionally support the X11 and maybe the Wayland protocol. It is developed by Canonical Ltd. and is intended to be the display server of choice for Ubuntu.
There is an implementation of the Mir display server available under the GPLv3, the libmir-server and the libmir-client libraries.
Quartz Compositor is the name of the component, that is fulfilling the tasks of a display server and of a window manager in the windowing system, that is being natively used by the Mac OS X family of operating systems.