Craig, he is talking about putting the handle in so it sticks out the other side of the head, it will change the direction of the bevel. I was always taught that the flat edge went toward the wood, this allows you to keep shaving wood off. I have seen it done both ways though. If the bevel is toward the wood it forces the cutting edge out of the wood so long cuts cant be made. It is just like the bevel on a draw knife. And I have seen them used both ways also.
riarcher, you have it figured out. The second one appears to be a lefty, but I'm not sure it isn't sharpened on both sides since it is a custom built axe.