Are Discipline and Punishment the same or is there a difference?

I was describing my thoughts on the differences between play, discipline, and punishment today and, while I was writing it out, thought that I would do a post and see what others out there think as well.
In my experience, the terms punishment, discipline, and play have been used

interchangeably in this lifestyle and I have come to believe that many don't understand the usefulness or distinction of them.
I believe that play is done strictly for fun. It can include some role play or scene play where the slave/sub/bottom is doing something to deserve punishment but it is strictly play and meant that way. The physical, verbal, emotional, or environmental ramifications are meant to be enjoyed.
I believe that it is the job of the Dominant to guide and educate the slave/sub and discipline and punishment are tools to accomplish this. If this isn't the motivation for the use of these tools, I believe that it is abuse and not guidance. I realize that some women want this but I don't believe that it is part of the M/s or D/s dynamic. I believe that many people call themselves Masters or Dominants to excuse the fact that they are abusive.
Discipline is meant to correct the behavior, thought pattern, or belief of a slave/sub. It is done in reaction to some form of disobedience, displeasing action/thought, or inadequate effort by the slave/sub that was not done willfully or purposefully. It was done through ignorance or accident. Here it is the Master/Dom's job to educate the slave/sub and teach them what they have done in error and what the correct path would have been thus eliminating the infraction in the future. The whole point of discipline is correction and frequently doesn't require any kind of physical reprimand or repercussions. An example of this would be if the Master/Dom asked for a tuna sandwich and the slave/sub interpreted this as a request for a tuna salad sandwich. If the slave/sub makes that sandwich with salad dressing like Miracle Whip and the Master/Dom did desire a tuna salad sandwich but only likes mayonnaise a correction is needed. The slave/sub would be mortified enough by creating displeasure in their master, as this was not intended, that discussion and clarification is all that is needed to ensure that the sandwich will me made correctly in the future. I realize that this is a very minor infraction but the idea holds. It was done without willfully or purposely attempting to displease the Dominant.
Punishment is used for when a slave/sub willfully or purposely displeases the Master/Dom. Here it isn't a matter of education, as they already new that their behavior, belief, or thought is unacceptable, it is a matter of re-education and motivation. Here the slave/sub did not consider the detrimental results of their actions to out weigh the benefit of them. This means that they must be taught that they were in error and the detrimental repercussions DO outweigh ANY benefit that they get from the action. Here the Master/Dom must find a punishment that is unpleasant enough for the slave/sub that they will never again wish to recreate this event. If the slave/sub is not dissuaded from the behavior by the mere fact tha it would displease their Dominant then additional motivation MUST be given to prevent a recurrence of this behavior in the future. As previously stated, punishment is to correct behavior, thought, action, belief. It should NEVER be pleasurable. If it is, the Master/Dom is, in fact, encouraging future episodes similar or identical to the infraction that made the punishment necessary. This being said, the Master/Dom must choose a punishment that fits the crime. If the punishment for a minor infraction is the same as a major infraction, the slave/sub loses the ability to believe that they are being treated fairly. This will inevitably lead to a lack of respect and trust in the Master/Dom which is NEVER a good thing. Respect and trust are the foundations of this lifestyle and dynamic. With proper use of discipline and punishment this can be built but if there is no distinction between them then trust and respect are eroded as the relationship becomes about play and fear rather than love and respect.