I think there is a bit of cross-talk in the punishment/no punishment thing. From what I can see it is a point of attitude and why sanctions are being imposed, not necessarily difference in the disciplinary actions. In same cases, the actions may be different, but in many cases they are identical. It seems to me that on occasion the 'we don't punish' camp can also come out with harsher consequences (e.g., instead of a week of no TV and a grounding, it could be no movies for years... which, I must say, I would in this case do -- no nighttime movies until the child's bedtime is later than the end of the movie).
Please correct me if I'm wrong, but my understanding of punishment is that a child does something wrong, and you impose a punishment geared to (1) indicate to the child that the thing was wrong, (2) cause some level of unhappiness, (3) hopefully prevent future repeats of the behaviour because the child wishes to avoid the imposition of the unhappiness, and (4) ideally, you prevent future misbehaviour in other realms as well, as the child understands similar unhappiness could be brought forth for any transgression.
My understanding of consequences is that a child does something wrong, and you either impose a logical consequence (fighting over the iPad, take away the iPad) or let a natural consequence occur (won't wear coat, gets cold) with the aim of (1) teaching the child what happens when they do that behaviour, (2) that the thing that happens is not to their liking (unhappiness), (3) hopefully prevent future repeats of the behaviour because the child wishes to avoid the outcome of their behaviour (unhappiness), and (4) ideally, teach the child to think about consequences of other behaviours and avoid inappropriate ones because they can calculate that the consequence will be not to their liking.
I suggest that the actions of the parents can be identical in many cases, and many people who apply punishments do so with logical consequences (it makes sense!). One difference is that arbitrary sanctions (no TV for fighting with sister) are not imposed in the non-punishment case (unless the fighting was over TV...), meaning that a child who moans about the 'unfairness' of a sanction may feel more justified if it is arbitrary; whereas when it is a logical consequence, they may still moan about the unfairness, but in doing so will have to confront their own behaviour and how it caused that. Another difference comes in point 4, above, where punishment can serve to cause children to simply know what will happen (parents impose punishment) if they do something they know is wrong, whereas without punishment it requires them to think more and they may end up pushing more boundaries if they are not capable of thinking through a logical consequence on their own. On the other hand, once this process is learned, they may be able to better identify inappropriate behaviours that haven't been expressly forbidden?
Sorry for the long tangent, here, but this is the sort of thing I've been trying to get my head around. I often see arguments where it seems that people assume no punishment means no boundaries, and then argue that if you do something that makes the child unhappy, you are in fact punishing. I think that the actions can be very similar, which is why people can get so worked up over it, as they feel someone is telling them to do something different when they know that doing something different wouldn't work very well. But as people talk past one another, they don't realise they are doing the same thing.