Reinforcement:
Adding or removing something to increase
the likelihood of a behavior recurring.
Punishment:
Adding or removing something to decrease
the likelihood of a behavior recurring.
Of the above, negative reinforcement is the trickiest to
understand, I think, and also the one least likely to show up naturally (without
following positive punishment). Increasingly, trainers are moving toward methods
that motivate the dog to engage in desirable behavior, noticing the behavior
they want and reinforcing that.
Whenever possible, I work with positive or motivational training, and in the
rare cases when I’m trying to extinguish a behavior that hasn’t responded to
other strategies, I may add positive punishment and with a lot of forethought. For
example, I do use head collars, and I make a soft hissing noise when my dog
barks excitedly for extended periods of time. Her initial startle reaction
allows me to redirect her to a more desirable behavior that I can reward
instead.
I wouldn't expect every person working with his or her own family dog(s) to fully grasp all of these concepts, but I do think that grappling with them, engaging in thoughtful conversations, and analyzing your own training methods and beliefs will help you make informed decisions when engaging with desirable and undesirable behaviors in your own home.