A proven way of influencing a horse's behavior is to reward desirable actions and punish undesirable actions. This is called operant conditioning. Note that this is all about consequences. Positive consequences for good behavior. Negative consequences for bad behavior. Notice also that this takes place entirely after the behavior has occurred.
Natural horsemanship uses operant conditioning but it also uses something else. Something that is proactive, that influences the behavior before it occurs. We describe it in different ways. We "set the horse up for success." We "make the right thing easy and the wrong thing difficult." We "make our idea become the horse's idea." This requires more mental engagement, planning, and commitment on the part of the trainer, but there are great rewards to be reaped.
One of the golden rules of natural horsemanship is to be as gentle as possible and as firm as necessary. Being proactive in training increases the opportunities to be gentle and decreases the need to be firm.