By the formal definition, a puppy mill is a large-scale breeding operation that produces large numbers of puppies for profit.
Not to mention the fact that by most accounts they are filthy and inhumane. Dogs are stock piled into cages which are unclean and unsanitary,with little nutrition and a lack of veterinary care. Most mills are run by people who care little about the breeding and more about the money. These dogs are kept in heat and are highly unsociable making these dogs miserable.
A breeder on the other hand has a in most cases a license from the AKC ( American Kennel Club) stating that both the parents are registered breeds. This however doesn’t state the quality or the health of the parents just their breeding. Also a breeder has medical histories and x-rays if the particular breed has hip and elbow issues. They should have a warranty and be open to calls and concerns. Paperwork from the AKC stating that the puppies have been registered with a full or limited registration. Full meaning can be bred and participate in performance activities. Limited meaning performance activities only.
My preference is adoption through a clean,well and registered society such as your local humane society or rescue group. You can always get references and complete factual medical history once the pet has been evaluated. Also you get to save a life and make a difference and change the world!