JKlastsky's quote is correct.
In behavioral terms, "reinforcement" (reward) is anything that causes a behavior to increase; "punishment" (correction) is anything that cause a behavior to decrease.
There are four ways to change a dog's behavior:
1. Give him something he wants (positive reinforcement)
2. Take away something he doesn't want (negative reinforcement)
3. Take away something he DOES want (negative punishment)
4. Give him something he doesn't want (positive punishment).
Note that "positive" and negative" mean adding or subtracting something to the dog's environment in this context.
"Punishment" and "negative" are emotionally charged words outside of the context of a formal discussion of the science of behavior, precisely because when done incorrectly, they leave an emotional residue that can adversely impact a training program. If too much "punishment" is used, and with bad timing, your dog may decide not to participate. At that point there is nothing that can be done about it except crank on the force, which isn't good for either the trainer or the dog. I don't think anyone here wants a dog that has to be forced to do something. Training your dog is supposed to be fun!
May I suggest reading Karen Pryor's book Don't Shoot The Dog
? It explains all of this in more detail that I should go into here (the post would be too long, "punishing" those who don't like to read long posts