NH is a philosophy that is about gaining trust and doing it incrementally thro sensitizing and desensitizing. Horses can become compliant as it is part of how they survive but there may not be a lick of trust.
Natural horsemanship is where you can give direction to the horse and he will respond with little aid and no tools.
Natural horsemanship shouldn't need any crops, sticks, spurs, anything. You should be able to work with your horse with little aid possible but the horse is listening.