Both types are referred to as being hypoallergenic dog diets. (dog-health-guide.org)
The correct name for these dogs that don't shed is hypoallergenic dogs. (dogsbarn.com)
Of course, there are some hypoallergenic dog breeds, but allergies can be triggered by so many other things such as your dog's saliva, the dander, or the pollen and dust that inevitably come along for the ride on your dog's coat. (notinthedoghouse.com)