The word Discipline comes from the latin word "Disciplina" meaning teaching or instruction. In modern culture it is often used as a synonym for punishment though, and that is far less of a useful skill.
This draws a line between to meanings of the word. Internal discipline and externally imposed discipline.
An example of externally imposed discipline would be military boot camp. Discipline in that context is doing what you are told, when you are told and not asking questions.
This is different from internal discipline which can't be learnt through having someone direct your actions and behaviours and using punishment to ensure compliance.
Internal discipline is learning to teach yourself, controlling your own behaviour and making the most of your own abilities. It is a skill that is gained through freedom and making your own choices.
External discipline is, in my opinion, far more superficial. Using punishment and strict direction can certainly give a strong impression of discipline, but in our current culture is that enough to set a person up for success?
Much of todays educational practices where designed with factory workers in mind during the industrial revolution. In that context external discipline was desired to keep people doing repetitive work grinding through the week.
In the martial arts much of the current practices have roots in military training. Japanese arts where used to prepare boys for service, most of the eastern styles where brought to the west by military personal.
If you want external discipline for your child, and kids in straight lines punching and kicking in sync... we aren't where you should go. That's not what we do or value.
Our flavour of martial arts by its very nature requires thinking and creativity under pressure. It requires adaptability and staying calm under pressure.
Confidence and self-discipline can only come from believing in yourself and your own ability to make choices and take action. Those things require freedom and with too much external discipline freedom to make choices disappears and confidence and self-discipline are never learned.
Now I am not saying external discipline should be completely removed. It definitely needs to be there at times, but the bigger lesson is choice. A child should learn that they can't run around screaming and making a mess in the store, but the lesson should be in empathy not fear of punishment.
Nor does punishment need to go entirely, missing out on something for being disruptive is a lesson as well. But the lesson can be you missed out because your choices caused other people to miss out when you where being disruptive.
So for us "discipline" is not about command and control alone. It is a teaching empathy, thinking under pressure and other behaviours that lead a person to be successful in life.