What you have pictured is generally called the Y/Z axis, although as you say it does vary. I always call X the axis the gantry runs on, so generally the longest axis.

The orientation of the rails in the image on the left is considered better since the deflection due to each bearing is more even. For forces in the direction pulling the bearing off the rail, not surprisingly, the bearings are weaker and will deflect more. If the open sides are facing, as you have drawn, this evens out so the deflection will be the same for all axis which is much better than having significantly different deflection which is what will happen if the rails are both the same way round.