Difference between Stage and MovieClip? and between Stage and Parent?

What is the difference between Stage and MovieClip? They are both display objects, right?

I have a MovieClip “A” containing a MovieClip “B”, (so A is B’s parent; and B is being shown inside A);

I did a trace, B.parent.name is “A”; and B.stage.name is “null”.
Could somebody explain to me why?

Thanks!!