I believe that everyone has a very different and personalised take on punishment and what it means to them. Some people say punishment, some say funishment, others even say abuse! So rather than try to tell you what it should be or what it technically is supposed to mean... I'll simply give you a little insight into my dynamic and D/s relationship with Sir and how we approach the term of punishment.
While we do essentially live within a 24/7 Dom/sub dynamic, we are also partners outside of the D/s and BDSM. Sir is just as much my life partner (We aren't married so I won't say husband but boyfriend sounds so childish when we have such a deep relationship!) as he is my Dominant. Now while these two sides of our lives intermingle and crossover each other, when it comes to the punishment they are vastly different. It would be borderline abusive for Sir to punish me in a BDSM sense for something that was an infraction of moral vanilla relationship rules.
Let's say for example that I was flirting with someone else, that's totally my choice to do that. Sir can't stop me from doing it, he can't say that no I can't speak to that person. And to us, it would be considered pretty well abusive if he turned around and punished me in some way for it. But it would be considered breaking the rules of our relationship, which would mean that we would sit down and discuss the issue and what that happening means for our relationship.
Now flip the coin, we are in bed and Sir starts a little head game with me. He starts whispering about how he knows I want another guy... How he knows I must be checking out the cute young bloke at work... How I must be daydreaming about having sex with him... I guarantee you I'll be a grovelling wet orgasming mess by the time he finishes setting this little scene in my head! Now for that, he may punish me. That little game he plays with me where I'm now in trouble for getting so wet thinking about having sex with someone else. To us, that is what punishment is. Punishment for us is more involved in the BDSM activities rather than our day to day D/s or relationship.
When we look at the D/s part of our relationship, the biggest and most horrible punishment Sir could ever inflict on me? Is his own disappointment. That is the only form of punishment, not that we even call it punishment, that we involve in our D/s. I know when I've messed up... Trust me, it's the worst feeling in the world! Just having to sit in front of Sir and listen to him discuss the thing I did wrong or the thing I forgot about and have him tell me how that made him feel... Oh, I'm usually in tears! Sir would agree with me here, there is absolutely no need for any other punishment when he knows for a fact that I'll be kicking myself for it anyway.
This brings us to the next part of that... When I know I've done wrong, I find it extremely difficult to forgive myself. Even if Sir has already discussed it and he himself is past the event, I will still be beating myself up over it at times. There are even times when Sir is very understanding of my mistake and can even tell me that there isn't anything for him to forgive. But sometimes I myself need to feel that I've had some sort of atonement for my misgiving. It's those times when I will actually ask Sir to give me something so that I can feel like I've payed for my mistake and that will allow me to move forward without the guilt eating at me. Sir is very careful in these times to make sure that I know that he is not punishing me and that I shouldn't think of it as punishment because there was nothing for him to forgive. He finds ways of allowing me to release that inner emotional turmoil over having made a mistake. It takes away the feeling like I need to beat myself up over whatever I've done wrong.
Sir is always very quick to remind me that I'm still his good girl and to reassure me that it's over with now. He will only give me as much as he thinks I need to move past it within myself. It's one of the things I love most about Sir, the fact he can read me well enough to know what I need. I trust him to know that, to know when enough is enough and to know exactly how to reaffirm in my head that I'm his good girl again.
So for us personally, we don't really use punishment within our D/s relationship. We most certainly don't use punishment within our vanilla part of the relationship. But we do enjoy punishment as a part of a mutually enjoyable part of our BDSM activities.