It's primarily based on course conditions. If these guys could've hit balls that stopped within 10 yards at The Open, they would have.
Any shot with a higher trajectory will land a bit softer, assuming all else is equal. So yeah, a cut will land a bit softer than a draw. Likewise, they might push the ball back in their stance just a touch to get a lower, running trajectory if they want it. But the dramatic difference you see at Muirfield vs. Muirfield Village is mostly due to course conditions.