Yep, I see the difference, momentum keeps them upright once they get up to one of the trotting or running gaits. I grew up close to Sportsmans and Hawthorne racetracks, so we always got a few minutes of racing film on the nightly news, mostly the harness meetings
And I'm just being a PITA for the helluvit, because it still looks to me that the poor critter on the charm is walking, otherwise its tail would be streaming out behind it (although maybe trotters and pacers have their tails held down somehow so the driver doesn't keep getting smacked in the face with a tail-full of horsehair). All my real-time race-watching experience has been with thoroughbreds rather than standardbreds.
And thanks for explaining!