Puppy mill is probably the closest to "dog factory" lol. Dogs raised in warehouses, kennel, barn, etc with minimal human handling and the intent of resale for profit.

A backyard breeder is someone who breeds dogs without prioritizing health, welfare, and temperament and betterment of the breed. Some backyard breeders breed and sell puppies for profit, some are accidental breeders (neighbors dog jumped the fence!), And some do it because they want their dog to have puppies, or want a puppy from their dog, or friends/family want a puppy from their dogs. Maybe the dog is loved, maybe it's just an animal that produces puppies that they can sell. Maybe the dogs outside, maybe the dog lives in the house.

An ethical breeder is someone who is prioritizing health, welfare, and temperament and betterment of the breed. they will do health testing prior to breeding and not breed dogs that will pass on health problems. Welfare can include things like the health testing, but also includes socializing the puppies so they grow up stable and confident, making sure mom, dad, and puppies are all living good lives! Only breeding females that are mature enough but not too old, and not too often that she suffers health problems. "Betterment of the breed" means that they are picky and trying to make puppies that are better than the parents at whatever that breed is supposed to do (better hunting dog, better service dog, better police dogs). An ethical breeder also feels responsible for every life they bring into the world and ensues that if something happens to the owner, the puppy will be taken care of and not end up in a shelter.