I don't understand the difference between current widget's context and overlay context.

Because in my app I want a second context to make some non-visible rendering and because framebuffer object doesn't help me (it inherits and affects screen framebuffer which is something I don't want), I ask about this overlay context.

What is for overlay context?
Is overlay context hidden?
Are there two completely separate contexts? (overlay and screen's context)
Can I render something to overlay context with no effect to screen?
Changes to overlay context (lightning, projection and modelview matrices etc) affect screen's context?

thanks