In the first picture, we can see a horse being lunged. As the handler points to the left, the horse moves to the left. The horse understands what the handler wants, which is to move in the direction being asked.
The handler's other hand is currently inactive, but can be used to drive the horse forward from behind if that extra pressure is needed.
In the second picture, we see a lady leading a horse through some obstacles. Let's observe the directions and positions of the horse and handler.
The handler is slightly ahead of the horse, but not by much. Her hands are very pronounced.
Look at where her active leading hand is. It is pointing to the right and is more forward than her non-leading hand. Why? Because the handler is asking the horse to stay to her right, encouraging it to go through the two obstacles instead of following behind her (the handler went around instead). She is also pointing her hand a bit more forward, because she is encouraging the horse to walk on or continue to move through the obstacles. She doesn't want it to stop, or back up, or do a fancy dance - she wants it to go FORWARD.
It was simple and clear. The handler wanted the horse to stay right and move forward. So that's what she asked for. You can see it in her hands!
Hope this helps, at least to some degree!