These two concepts go hand and hand so it is easiest to learn about them together:
Escape conditioning - The process of teaching or conditioning a dog (or any creature) how to escape the discomfort of a punishment by performing a desired behavior.
Avoidance conditioning - The process of teaching or conditioning a dog how to completely avoid the possibility of a punishment.
In general it is best to teach a dog how to escape a correction, before we teach that dog how to avoid that correction.
If a dog does not know how to escape a correction you may get panic behavior ranging from flight, learned helplessness, and even handler aggression. Often the dog will just freeze up when punished because he simply does not know what to do to make it stop. All of these behaviors can be misinterpreted by a handler as the dog being stubborn or defiant. This is a mistake because a frustrated trainer's actions to a dog he feels is falsely disobedient will cause more and longer lasting side effects.
Invisible fence systems - We want to concentrate on teaching the dog how to escape the correction (run toward the inside of barrier once corrected), before we concentrate on teaching the dog how to completely avoid the correction.
If the dog did not learn how to run toward the yard when corrected, he may continue through the invisible barrier if he accidentally comes too close to the boundary. Since the electric correction goes away on either side of the boundary, the behavior of crossing to the wrong side may become the habit for escaping an invisible fence correction.
Obedience commands - We want to teach the dog how to escape a correction (move into a sit position to release the pressure of a training collar), before we teach the dog how to avoid the correction.
If the dog did not learn this first, he may panic and possibly bite the handler, which may also make the correction go away. But, the trainer's reaction to this bite may add to future problems with the relationship and training.
Escape conditioning emphasizes the "negative reinforcement" (removing something to encourage a behavior) part of operant conditioning. Although, it is not the same exact thing. Escape conditioning can include other operant conditioning quadrants, such as positive reinforcement, to prompt the dog toward the desired behavior needed to escape the punishment applied during negative reinforcement. Once the dog understands how to respond the correct way to the negative reinforcement, without additional help from other types of prompts, escape conditioning for that particular punishment is considered complete.
Avoidance conditioning has an emphasis on the "positive punishment" part of operant conditioning (adding something to discourage behavior). It too can include other quadrants of operant conditioning during this process. Only when the dog clearly understands and is consistently successful at avoiding the punishment associated with a wrong behavior is the avoidance conditioning for that particular exercise complete.