Window system
The layer that shares one screen, keyboard and mouse among several programs by giving each a rectangle to draw in and routing input to whichever one the pointer is over.
The idea came out of the Xerox Alto, where Smalltalk had overlapping windows sharing a bitmap display in the mid-70s. Through the 80s every platform grew its own: Apollo's Display Manager in 1981, the Macintosh and X in 1984, SunView, Amiga Intuition and Windows in 1985, Sun's NeWS in 1986. What they have in common is the job: keep track of which window is where, draw primitives and text, deliver keystrokes and clicks to the right recipient, and repaint whatever was covered once it is exposed again.
Where the lines are drawn varies. X puts everything in one user-space server process and leaves appearance to a separate window manager; Windows moved its graphics code into the kernel with NT 4.0 in 1996 for speed; macOS Quartz and Wayland let a compositor own the screen while programs render into their own buffers. Above it there is always a widget toolkit that turns rectangles into buttons, and above that a desktop environment. "Display server" names the same layer seen from the protocol side.