How to redirect all OpenGL output?

I wrote a minimal OpenGL application and linked the console to the project. OpenGL outputs its Version and things like that to the console.

The small OpenGL framework that I am writing will be used by an aplpication that features its own logging so i want to redirect all logging to there.

So far I tried googling the problem but I can not find all the information I need. There are debugging tools, but those are stand alone. I found logging options but it is not clear to me if this is meant to catch all messages or just some.

void glDebugMessageCallback​(DEBUGPROC callback​, void* userParam​);

Will registering with this function catch all messages or will I miss some of them. If so, how do I log everything?