Windowing system on El Capitan, and XQuartz
XQuartz is a windowing system on its own, just installing it doesn't change anything. If you need to run application requiring X11/XQuartz, you need to start the Xquartz app (aka X11 server) before you start the application. The X11 server will then run "on top" of OS X, so the behaviour of other applications doesn't change.

See also What is XQuartz? for more details.