Question: Are Cairn Terrier and American Pit Bull Terrier both dog breeds?
Context: The Teddy Roosevelt Terrier is a small to medium-sized American hunting terrier.  Lower-set with shorter legs, more muscular, and heavier bone density than its cousin the American Rat Terrier.  There is much diversity in the history of the Teddy Roosevelt Terrier breed and it shares a common early history with the American Rat Terrier, Fox Paulistinha and Tenterfield Terrier.  It is said the Rat Terrier background stems from the terriers or other dogs that were brought over by early English and other working class immigrants.  Since the breed was a farm, hunting and utility dog there was little to no planned breeding other than breeding dogs with agreeable traits to each other in order to produce the desired work ethic in the dog.  It is assumed that the Feist (dog), Bull Terrier, Smooth Fox Terrier, Manchester Terrier, Whippet, Italian Greyhound, the now extinct English White Terrier, Turnspit dog and or Wry Legged Terrier all share in the Teddy Roosevelt Terrier's ancestry.  These early Ratting Terriers were then most likely bred to the Beagle or Beagle cross bred dogs (for increased scenting ability) and other dogs.  Maximizing the influences from these various breeds provides the modern Teddy Roosevelt Terrier with a keen sense of awareness and prey drive, an acute sense of smell and a very high intellect.  Although they tend to be aloof with strangers they are devoted companion dogs with a strong desire to please and be near their owners side at all times. The Chamuco (a Mexican word which means "devil") or Mexican Pitbull is a dog breed not recognized by any Canofile association.  It originated in the center of Mexico, it was developed in this country in the 1970s, product of the accidental or intentional crosses of the American Pit Bull Terrier with the now extinct Mexican Bulldog, street dogs, American Bully, Pitbull Blue, Staffordshire bull terrier, American Staffordshire Terrier, and probably with the Boxer.  Its name comes from the Mexican slang "Chamuco", which means devil because of its temperament and tenacity.  Also it called Mexican pitbull or miniature pitbull, but actually is Dogo of Mexican origin. The American Pit Bull Terrier (APBT) is a dog breed.  It is a medium-sized, solidly-built, intelligent, short-haired dog whose early ancestors came from the British Isles.  When compared with the English Staffordshire Bull Terrier (another breed within the type commonly called pit bulls), the American Pit Bull Terrier is larger by margins of 6 - in height and 25 - in weight.  The American Pit Bull Terrier varies in size.  Males normally are about 18-21 inches (45–53 cm) in height and around 35-60 pounds (15–27 kg) in weight.  Females are normally around 17-20 inches (43–50 cm) in height and 30-50 pounds (13–22 kg) in weight. Daddy (1994 ‒ February 19, 2010) was an American Pit Bull Terrier integral to dog trainer Cesar Millan's work and his television series, "Dog Whisperer".  Daddy became known for his calm temperament, tolerance for smaller dogs and capacity for empathy. The American Dog Breeders Association(also known as ADBA) was started in September 1909 as a multiple breed association.  The residing president, Guy McCord, was an avid fancier and breeder of the American Pit Bull Terrier and was a close friend of John P. Colby.  Colby was the mainstay of the ADBA and therefore it was considered the "home" registration office for the Colby dogs.  All members in good standing could register their dogs and litters for the yearly fee of $2.50.  The exclusive member’s idea gradually was replaced by a registry open to all owners and breeders of purebred dogs.  Over time the association focused on the registration of the American Pit Bull Terrier. The Cairn Terrier is one of the oldest terrier breeds, originating in the Scottish Highlands and recognized as one of Scotland's earliest working dogs.  The breed was given the name Cairn, because the breed's function was to hunt and chase quarry between the cairns in the Scottish highlands. The Bull and Terrier is a breed of dog that was the progenitor of the American Pit Bull Terrier, American Staffordshire Terrier, English Bull Terrier and the Staffordshire Bull Terrier. Ch.  Rocky Top's Sundance Kid ("aka: "Rufus"") (April 8, 2000 – August 9, 2012), is a Bull Terrier who is best known for being the 2006 Best In Show winner at the Westminster Dog Show.  He is the first Colored Bull Terrier to win Best in Show at Westminster, with the only other victory for his breed going to a White Bull Terrier in 1918.  He also won Best in Show at the National Dog Show in 2005, and on retirement trained as a therapy dog.  He is the most successful Colored Bull Terrier Show Dog of all time. The Airedale Terrier (often shortened to "Airedale"), also called Bingley Terrier and Waterside Terrier, is a dog breed of the terrier type that originated in the valley ("dale") of the River Aire, in the West Riding of Yorkshire, England.  It is traditionally called the "King of Terriers" because it is the largest of the terrier breeds.  The Airedale was bred from the Old English Black and Tan Terrier (now extinct), the Bull Terrier, the Otterhound and probably some other Terrier breeds, originally to serve as an all around working farm dog.  In Britain this breed has also been used as a war dog, guide dog and police dog.  In the United States, this breed has been used to hunt big game, upland birds, and water fowl, and serve in many other working capacities. Pit bull is the common name for a type of dog.  Formal breeds often considered in North America to be of the pit bull type include the American Pit Bull Terrier, American Staffordshire Terrier, American Bully, and Staffordshire Bull Terrier.  The American Bulldog is also sometimes included.  Many of these breeds were originally developed as fighting dogs from cross breeding bull-baiting dogs (used to hold the faces and heads of larger animals such as bulls) and terriers.  After the use of dogs in blood sports was banned, such dogs were used as catch dogs in the United States for semi-wild cattle and hogs, to hunt and drive livestock, and as family companions.  Despite dog fighting now being illegal in the United States, it still exists as an underground activity, and pit bulls are a common breed of choice.
Answer: yes