Owners are trained to use behavior modification techniques too, in most programs. The most popularly know practitioner is one who has a board certification in the veterinary field. Most behavior problems such as chewing, digging, barking, separation anxiety, aggression, and housetraining need a behavior consultant not a trainer. Consultants help the animal to learn, not to just respond, and they recondition or retrain appropriate behavior. Sometimes there will be alternative therapy prescribed with the assistance of your veterinarian.
Training usually involves getting the animal to respond or react to a cue or stimulus on command.
There are many types of trainers out there. Many will train the dog without you, but there are those who will train you to train the dog too. Usually they have a specialty in a couple of different areas. Some training practices are steeped in tradition and are handed down to the apprentice or taught to them in a more formal manner. Some still use harsh methods, others use food reward and conditioning, methods are just tools to use.