Anim8or Community

The documentation describes the small buttons X, Y, Z as shows the three axis of the 3D world.
They indicate which axes are "unlocked', allowing you to move and rotate things in each
direction. You can individually select or deselect them, and thus restrict the movement
of objects that you are changing.
And the cross arrows button as
This is the move function. You set it when you want to move your objects around
on the screen. When you press the left mouse button within a view window you
can drag anything that is currently selected in the X and Y directions by moving
the mouse to the left and right, or up and down. The objects will move along with
your mouse. Similarly, the right mouse button will move them along the Z-axis,
which is usually into the screen.

But, in fact, at least in windows 7, the x,y,z axis refer to the screen not to the 3D world axis.
This is, the movements X,Y are left-right, top-bottom of the screen, and Z back and front respect to the screen too, not respect to the 3D world axis.

If you change your view from front to left, right, bottom, top, then your mouse left button will move things up down and sides as it is the x-y of the screen, but the 3D world affected coordinates and new object coordinates will be in Z axis since you gave a turn to it, no matter if you have restricted the Z coordinate with the toolbar buttons, what it is restricting is the use of the mouse right button.

So do not be confused, the X,Y,Z toolbar buttons, just restrict the mouse moves in the axis respect to screen not to 3Dworld
In Ortho view, only uses the mouse left button to move all around the 3 axis, so if you restrict the mouse moves in x,y with the toolbar buttons, you neither will be able to move the object in Z axis, unless your are using it for rotating the object and use the right mouse button and it is not locked in the toolbar

So, in other desdription the x,y,z toolbar buttons are left-right, up-down, front-back moves.