GLcore was once the name of the Mesa-based software renderer used by the X server for indirect GLX contexts. When AIGLX was added, the X server could instead use a DRI driver for the indirect renderer; GLcore remained as a special build of Mesa for the software GL case. Starting with xserver 1.5 the server instead uses the same interface to software drivers as libGL, and GLcore is no longer built.

This all has nothing to do with OpenGL core contexts (with the exception that, since Xorg only implements GLX protocol supporting through OpenGL 1.5, it is not possible to create an indirect core context even if the same driver could support a direct core context).