Why are bone axis and poseBone axis different?

Hi, I’m trying to write an exporter for a format in Blender. I’m actually stuck at bones and animations.

So here’s where my question comes. PoseBones transformations are made in their own axes. That’s ok, but I found something weird for me: the bone (PoseBone.bone) has different axes than the poseBone!

http://i.imgur.com/e935jNJ.png

Another weird thing about it is that marking “Axes” in the Display properties of the Armature shows the poseBone axes, both in pose and edit mode:

http://i.imgur.com/CgZdvNl.pnghttp://i.imgur.com/4e6tf8g.png

So, what are the bone axes for?
The only relation I’ve found is that they are equal to the bone matrix, which (as far as I know) is relative to the bone parent.
http://i.imgur.com/y3fYC9Q.png

Here is the whole armature:
http://i.imgur.com/yhwghl4.png

The pbone matrix is in relative to the rest pose, and it is an identity matrix because you have no pose / transformation applied.

That’s matrix_basis. I was talking about x_axis, y_axis and z_axis.