The corridor of aids gets more sophisticated along with the games we want to play. When we move from heeding on the ground to working the horse under saddle, the aids or pressures have to change. The horse can't see the handler anymore so the handler can't influence the horse visually by changing their body position. When the trainer changes position in the saddle, their body creates physical pressures on the horse's body. The trainer gradually starts substituting the feel of specific physical pressures from the bit, the legs, and the seatbones for the feel that the visual pressure that moving their body when they were on the ground put on the horse. But the training is still about using a corridor of pressures to create a feeling that helps the horse take the shape we want. And it's still about directing every step the horse takes.
You have to ride every stride. The more sophisticated the game or action the handler wants, the more critical it becomes that the handler pays attention to every step the horse takes. A good rider directs every stride with a corridor of aids that tells the horse the direction of the stride, the length of the stride, and the cadence or how many strides to take in a particular segment of time. The rider-trainer may not actively do something to influence every stride. There will be times when everything is going right that they'll just sit there and let the good strides roll. But they will always be aware of each stride, allowing each correct stride, and be ready to influence the next stride in order to achieve the shape they want and play the game they want.
All this directed attention is hard work. A lot of people don't understand how mentally intense even what looks like simple groundwork can be for both the handler and the horse. That's why you never make a baby horse's early work sessions very long. Some horses can only take a few minutes in the very beginning. They have to work up to a longer attention span. When you start them under saddle, you may have to shorten their work sessions again and work them back up to more time. Every horse will be different.
When things start to go wrong in a training session, it's usually because the trainer had a lapse of attention. They took their attention off the horse so the horse's attention wandered, too. Or the handler had a mental lapse that made the corridor of aids too fuzzy for the horse to get the feeling of the shape the handler really wanted. It's not a disobedience on the horse's part. It's a lapse of obedience because the trainer let the horse's attention wander.
Whether you are working with him on the ground or up on his back, if a horse takes even a single step you did not direct him to take, mentally it's the equivalent of him running away. When you're with a horse, you have to give him your complete attention in order to get his.