Is X11 the default display server application on Mac OS X?

Quartz is the low-level graphics layer, and the WindowServer process manages windows on top of it. Both are Apple proprietary software.

From here:

Two interacting systems create and manage Cocoa windows. A window is created by the window server. The window server is a process that uses the internal window management portion of Quartz (the low-level drawing system) to draw, resize, hide, and move windows using Quartz graphics routines. The window server also detects user events (such as mouse clicks) and forwards them to applications.

OSX (Server or standard) shows on the attached monitors using the Aqua layer in OSX. You can attach to the server from other machines using X11 apps or VNC/Apple remote to the server.

OSX does not have a separate app to display the screen as X11 does - any app can call calls through the Aqua layer to display on the scrren. See Apple's OSX architecture overview