My understanding, from the information I have at hand as I have been pondering the same question, is that the position with the left arm across the body with the lock in the crook of the arm is 'Support Arms', the right hand on the stock is part of the maneuver from 'Shoulder Arms' and is normally repositioned to the side of the body, although a slight pose variation is to have the right hand holding the stock.
The 'shoulder Arms' position is the more normal for route marches as it would be somewhat more comfortable.
It seems to be a way of differentiating the arm positions of different nations but, as I understand it, all drill manuals were similar. However the supposed 'March Attack pose is popular with wargame figures but is not actually a correct position.
Hope that helps.
Simon