Some terms below are universal and are used legally. Some terms are slang.

Sentient being 
A being is considered ‘sentient’ if he or she (human or nonhuman) can experience suffering, physically or psychologically, due to the fact that they have a nervous system and a brain. (Sentience relates to ‘senses.’)

Companion animal 
Animal, such as a dog, cat, bird or rabbit, that provides companionship to a human. Minn. Stat. Sec. 343.20 Subd. 6 defines a pet or companion animal as "any animal owned, possessed by, cared for, or controlled by a person for the present or future enjoyment of that person or another as a pet or companion, or any stray or pet or stray companion animal."
 
Service animal
The American with Disabilities Act (ADA) defines a service animal as “any guide dog, signal dog, or other animal individually trained to provide assistance to an individual with a disability.”

Commercial breeder — general
Someone who owns or leases multiple intact female dogs or cats and produces litters of puppies or kittens with the intent to make a sale. "Commercial" implies business or commerce. This type of breeder breeds dogs or cats as a business for profit. Commercial breeders could be reputable and smaller with, typically, a focus on one breed. These type of breeders work closely with the new "owner/caretaker" of the animal to ensure the animal will be treated well. Commercial breeders, by definition, can also be substandard or negligent with a low or high volume of dogs, several breeds, and inadequate or horrendous conditions — known as puppy or kitten mills. With larger commercial breeding facilities, staffing is often inadequate (based on volume of animals), resulting in minimal observation and care of each animal animal due to low staff-to-animal ratios. Many commercial breeders advertise or sell directly to consumers through the Internet and do not allow consumers to view their animals in the kennels.

Commercial breeder — by Minnesota statute

The MN Commercial Breeders Licensing and Enforcement law, for purposes of licensing and regulation, defines a commercial breeder as (Minn. Stat. sec. 347.57 subd. 5):

"Commercial breeder" means a person who possesses or has an ownership interest in animals and is engaged in the business of breeding animals for sale or for exchange in return for consideration, and who possesses ten or more adult intact animals and whose animals produce more than five total litters of puppies or kittens per year.

Puppy mill 
Slang developed in the 1960s. Describes a type of breeder who mass produces dogs and, in order to maximize profits, is known to cut corners in breeding operations resulting in harm and suffering to the animals. Primary motive is not the well-being of the animal. The puppy mill owner views dogs as commodities or products. This attitude and, often, lack of animal husbandry skills creates substandard (often deplorable) conditions that harm the physical and emotional health of dogs and puppies. Substandard conditions include lack of veterinarian care or breeding plan, unlimited puppy production, no screening for genetic diseases, unsanitary facilities, unsafe and cramped cages, no environmental stimulation or human contact with animals, inadequate ventilation and temperature, poor quality food and water, poor quality shelters and no bedding. Typically, puppy mills are hidden behind “no trespassing” signs and will not allow consumers on the property to view the animals or conditions. See inhumane breeding.

Kitten mill or cattery
Same as puppy mill but for cats and kittens.

Brood bitch
Also known as breeding stock. A brood bitch is a female dog used for breeding. It has both good and bad connotations, depending on the intent and purpose of breeding. Reputable dog and cat breeders use the term to describe females with a good pedigree to be bred selectively and with care; though even some reputable breeders harm the mother with too many litters or too many c-sections. Inhumane breeders buy females at auctions, keep the female caged their entire life, breed them at each cycle (starting at 6 months of age) and, when the female can no longer get pregnant or carry the puppies, is sold back into the ‘system’ or killed.

Class A
‘Class A’ is used by the USDA and refers to licenses given to breeders and deal only in animals they breed and raise.

Class B
‘Class B’ is used by the USDA and refers to licenses given to brokers, bunchers and operators of auction sales. Auction operators do not take physical control or possession of the animals.

Class C
‘Class C’ is used by the USDA and refers to licenses given to animal exhibitors.

Animal Dealer
The USDA sometimes uses this word as a catch-all, categorizing pet breeders, pet wholesalers, animal brokers, auction operators, hobby breeders, public pounds, private shelters, boarding kennels and others as dealers — dealing with animals.

Retail pet store
A retail pet store may vary based on the merchandise sold. Some retail pet stores sell domestic animals to pet owners; others refuse to do so and only sell pet supplies and may offer "adoption days" where rescue groups show and "adopt out" animals.
NOTE: The USDA has exempted traditional 'retail pet stores' from licensing — with the assumption that the consumer gets to see/evaluate the puppy of kitten at the pet store. In 2013, the USDA changed the definition of "retail pet store" to include certain animals sold through the Internet and phone. For details, go to: AWA licensing

Direct sales
Selling domestic pets directly to pet owners.

Pet Wholesaler
Anyone trading, buying, selling or importing pets in wholesale channels.

Animal Broker
A person, firm, partnership, corporation or association that purchases animals for resale to other brokers or pet dealers. They’re the middlemen, who buy from commercial dealers and sell to retail outlets or other businesses/organizations. They coordinate the transport with the carriers, shipping by the crate-load or truckload.

Animal Exhibitors
Businesses that feature animals in performances or use animals on display to the public, including zoos, petting zoos, circuses and other exhibitions.

Auction Operators
People who operate auctions where animals are bought and sold.

Carriers
Businesses that transport animals for hire, including airlines, shipping lines, railroads and other means.

Buncher
Lowest on the evolutionary scale. Bunchers steal or collect dogs to sell to research laboratories, to be as bait used in dog-fighting rings or for breeding stock in puppy mills or catteries. Bunchers respond to ads that say “free to a good home” or purchase very cheap animals and sell for more money.

Animal hoarding

See Hoarders

NOTE: Beware. Just as with any issue, people recognize the power of words and use them to convey their own truth. A recent story from a commercial kennel breeders’ magazine encouraged breeders to use the correct “vocabulary” when selling their dogs, so as not to create a negative image. Examples cited: Use ‘breeding animals’ instead of ‘breeding stock;’ use ‘sire and dam’ instead of ‘stud and bitch;’ use ‘pet animal distributor’ instead of ‘broker or B dealer;’ and use ‘kennels’ vs. ‘hutches’ (rabbits live in hutches; dogs live in kennels).