Canon EOS 5D Mark III Instruction Manual (en)

 Customizing AF FunctionsN
You can set the AF area selection mode and manually-selected AF 
point separately for vertical shooting and horizontal shooting.
: Same for both vert/horiz
The same AF area selection mode and 
manually-selected AF point (or Zone) are 
used for both vertical shooting and 
horizontal shooting.
: Select separate AF points
The AF area selection mode and manually-selected AF point (or Zone) 
can be set separately for each camera orientation (1. Horizontal, 2. 
Vertical with the camera grip at the top, 3. Vertical with the camera grip 
at the bottom). Convenient when, for instance, you want to keep using 
the right AF point during all camera orientations.
When you manually select the AF area selection mode and AF point (or 
Zone with Zone AF) for each of the three camera orientations, they will 
be set for the respective orientation. Whenever you change the camera 
orientation, the camera will switch to the AF area selection mode and 
manually-selected AF point (or Zone) set for that orientation.
Orientation linked AF point
If you clear the camera settings to their defaults (p.56), the setting will be 
[Same for both vert/horiz]. Also, your settings for the three camera 
orientations will be cleared and all three will revert to Single-point AF 
(Manual selection) with the center AF point selected.
If you set this and later attach a lens from a different AF group (p.79-85, 
especially Group H), the setting may be cleared.