Terminology and the meaning behind it.
Correction - The act or process or correcting. Correcting - To remove the errors or mistakes from.
The meaning of correction in dog training - To punish for the purpose of improving or reforming.
Very different. Back in the old days as a typist I was often returned a report I'd typed out with corrections on it. This was simply something that came with the job. It was either a typo on my part (not often that is) or a rewrite by the scientist dude. I worked at National Defense in Canada for many years; before my full on dog days. "These are the corrections" they'd say as they handed me back the report. I was to redo the words or phrases that were circled. Can you imagine if I got a yank on a chain around my neck every time I made a mistake? No, nor can I.
In conventional choke collar training, a correction is a yank on a collar. Depending on the person training, a yank can be a tiny one to an almighty knock the dog off their feet type of yank. It is typically delivered for any behavior that is unwanted. There is not a great deal of education offered from the owner/trainer. It is more of a "don't do that," type thing.
The term 'correction' is not used in positive reinforcement training. There is no such thing. Instead it is replaced with an error marker. Some PR trainers don't use error markers but I do. I feel that the more information you can give to your dog the better. Why leave them searching for an answer to getting a treat with no hints as to what they are doing? Best to let them know what is an incorrect offer of a behavior so that they can move on to the next.
When a person takes the time to learn how dogs learn they discover a better way. Sure corrections work; if you got a yank on the neck every time you reached for a cupcake on the counter, you would stop. Now depending on how good those cupcakes (if it were one of my amazingly delicious ones) were and the level of your desire you might not stop right away. This would then mean that you'd receive more harsh yanks on your neck. Perhaps so hard that you would fall to the ground. Would you stop then? Maybe not. This is where it can get scary. Then what? What does a conventional choke collar trainer do when the escalation of yanks stop working? The answer is that it gets physical.
Frustration grows when we try and try and try without results. Do we ponder the idea of error on our part, not likely. The trainer delivering the harsh yanks thinks that their dog is deliberately defying them, trying to dominate them. Resentment builds and the horrible cycle of the challenge begins.
When I was walking in Newport beach the other day Elsa stopped on a dime to take a whiff of something that had caught her nose. I stopped and let her take it in when a man walking by said "oh someone has a mind of her own" as I was still facing our walking direction and Elsa had turned. I smiled my "stupid" smile and we proceeded along. I stored that statement in the back of my mind to ponder on later. The whole idea of a dog having their own mind really bothers some people. This has been something that bothers me for years. Often I will tell owners that my training does not work around the robot scenario. Dogs are not robots and yes they do have their own mind.
A dog's mind is quite regularly smarter than a human mind. They keep it simple, black and white whereas we confuse things in our emotional minutia. Dogs are amazingly intelligent, so why do humans think that they should not have their own mind or thoughts? My thought on the question is that many humans with their inferior mind have yet to realize just how exceptional the canine mind is.