A highly trained dog is a dog that has experience performing a given skill or skill set, provided through many successful repetition. Most commonly the dogs that impress us when we observe their obedience clearly understand the conceptof obedience, which is easily hedonically understood by the dog as "my behaviour produces outcomes, therefore I control the outcomes through my actions".

Highly trained dogs typically display classically conditioned obedience, and typically perform those skills it has learned with a high degree of accuracy and expediency.

A dog withhighly proofed obedience is the next step in the training process. A dog with highly proofed skills or skill sets will perform typically perform those skills it has learned with a high degree of accuracy, expediency, and reliability.

To claim that a dog is highly proofed in a given skill is to say that it has been tested in a great many environments, under a great amounts of highly varied distraction, and great amounts of potential duress.

For a sporting dog, proofing of a given skill often times ends at a level that will allow it to compete successfully in it's given sport. Clearly, in a sport like Sch, the level of proofing tends to be much much less given that the distractions a dog is likely to encounter tend towards being predictable.

In sports like Belgian Ring, Mondio Ring, etc, the unpredictable variety of the distractions and potential duress clearly requires a great deal more proofing, even for dogs at the lower level.

For a dog working operationally in any non-government service role, such as PP/Sec work, proofing of skills is the major difference between a safe dog (for the dog and the community) and a liability on the leash; this goes equally for the offender work and the obedience.

A dog that will recall promptly and responsively, with properly classically conditioned obedience and a high level of proofing, will always be more of an asset to himself, his handler, his family, and his community, than a dog that is simply highly trained.

The ideal picture? A highly proofed dog that also displays great attitude and joy in performing his commanded task.

Proofing equals reliability, and reliability is far undeniably far more important than the appearance of a given skill in all but a competitive sporting or obedience dog. As responsible dog trainers of dogs (and PP/Sec dogs especially) I think that this understanding needs to be reflected in what we teach and preach to our clients and the dog training community at large.
Just one man's opinion...