Not sure it's that. The vibration and sound is not punishment, the electrical stimulation is not really punishment either, though it causes a degree discomfort if set appropriately: at the lowest setting that the pup notices.
It's a terminology thing. Operant conditioning is well defined. Positive means to add something that effects behaviour, e.g. positive reinforcement you give a treat or whatever to reinforce the wanted behaviour. Positive punishment, you add a stimulus of whatever kind that makes the behaviour less likely to occur. If it works to decrease the likelihood of the behaviour it is "punishment". It does not have to be severe, it just needs to have an effect.
Negative reinforcement, you are removing something, i.e. taking away a stimulus when you get the desired effect, negative punishment you take away something the animal wants, which decreases the likelihood of the behaviour.