Question: Are both Beagle and Cavalier King Charles Spaniel types of dogs?

Context articles: Canine Chiari-like malformation
Beagle
Rex (dog)
King Charles Spaniel
Cavapoo
Dash (spaniel)
Masticatory muscle myositis
Cavalier King Charles Spaniel
Toy Trawler Spaniel
Beaglier

Chiari-like malformation (CM) is the most common cause of foramen magnum obstruction and syringomyelia in dogs.
 Syringomyelia (SM) is a disease of the spinal cord typified by fluid filled cavities, or syrinxes, within the spinal cord substance.
 The disease is caused by the obstruction of cerebrospinal fluid (CSF), in the nervous system.
 A situation of high pressure in the spinal cord compared to low pressure outside, leads to fluid accumulation, which eventually forms cavities.
 CM is a condition characterized by the mismatch of size between the brain and the skull.
 The skull is too small causing part of the brain to descend out of the skull through the opening at its base, crowding the spinal cord.
 The cause of CM is not yet fully understood.
 CM is rare in most breeds but reportedly has become very widespread in the Cavalier King Charles Spaniel and the Griffon Bruxellois (Brussels Griffon).
 Some researchers estimate that as many as 95% of CKCSs may have CM.
 It is worldwide in scope and not limited to any country, breeding line, or kennel, and experts report that it is believed to be inherited in the Cavalier King Charles Spaniel.
 CM is so widespread in the Cavalier that it may be an inherent part of the CKCS's breed standard.
 This disease not only affects thousands of dogs, but a similar condition affects over three hundred thousand children yearly.
 Therefore, canines are an appropriate model for the treatment of the human condition.
The Beagle is a breed of small hound, similar in appearance to the much larger foxhound.
 The beagle is a scent hound, developed primarily for hunting hare.
 With a great sense of smell and superior tracking instinct, the beagle is employed as detection dog for prohibited agricultural imports and foodstuffs in quarantine around the world.
 The beagle is intelligent but single-minded.
 It is a popular pet due to its size, good temper, and lack of inherited health problems.
Rex (December 16, 1984 – August 31, 1998) was a Cavalier King Charles Spaniel owned by Ronald Reagan and his wife Nancy during his term as President of the United States.
The King Charles Spaniel (also known as the English Toy Spaniel) is a small dog breed of the spaniel type.
 In 1903, the Kennel Club combined four separate toy spaniel breeds under this single title.
 The other varieties merged into this breed were the Blenheim, Ruby and Prince Charles Spaniels, each of which contributed one of the four colours available in the breed.
The Cavapoo (also known as a Cavoodle) is a crossbreed dog, the offspring of a Poodle and a Cavalier King Charles Spaniel.
 The Cavapoo became especially popular through crossbreeding programs in Australia in the late 1990s.
 The Cavapoo has since become one of Australia's most popular breeds.
 Cavapoos were bred by ACA Breeders kennels to be healthy, outgoing, small dogs with a low to non-shedding coats, who would get along well with children.
 They are a very popular crossbreed dog in Australia due to their exceptional temperaments, robustness and low-shed.
 The breed is also increasingly popular in the United Kingdom.
Dash (1830–1840) was a Cavalier King Charles spaniel owned by Queen Victoria.
 Victoria's biographer Elizabeth Longford, called him "the Queen's closest childhood companion", and in the words of the "Oxford Dictionary of National Biography", he "was the first in a long line of beloved little dogs".
Masticatory muscle myositis (MMM) is an inflammatory disease in dogs affecting the muscles of mastication (chewing).
 It is also known as atrophic myositis or eosinophilic myositis.
 MMM is the most common inflammatory myopathy in dogs.
 The disease mainly affects large breed dogs.
 German Shepherd Dogs and Cavalier King Charles Spaniels may be predisposed.
 There is a similar disease of the eye muscles found in Golden Retrievers. Symptoms of acute MMM include swelling of the jaw muscles, drooling, and pain on opening the mouth.
 Ophthalmic signs may include third eyelid protrusion, red eyes, and exophthalmos (protruding eyeballs).
 In chronic MMM there is atrophy of the jaw muscles, and scarring of the masticatory muscles due to fibrosis may result in inability to open the mouth (trismus).
 The affected muscles include the temporalis, masseter, and pterygoid muscles.
 The disease is usually bilateral.
The Cavalier King Charles Spaniel is a small spaniel classed as a toy dog by The Kennel Club and the American Kennel Club.
 It originated in the United Kingdom and is one of the more popular breeds in many countries.
 Since 2000, it has grown in popularity in the United States and ranks as the 18th most popular pure-breed in the United States (2013 Registration Statistics).
 It has a silky, smooth coat and commonly a smooth undocked tail.
 The breed standard recognizes four colours: Blenheim (chestnut and white), Tricolor (black/white/tan), Black and Tan, and Ruby.
 The breed is generally friendly, affectionate and good with both children and other animals; however, they require a lot of human interaction.
 Since they are a family dog, it is recommended to not leave them alone for long periods at a time.
 The expected average lifespan of a Cavalier King Charles Spaniel is under ten years.
The Toy Trawler Spaniel is an extinct breed of Spaniel which physically was similar to the King Charles Spaniel of the 16th century.
 It is considered to have descended from the original King Charles Spaniel, and the older variety of Sussex Spaniel.
 It was originally used as a sporting dog, but became used as a toy and show dog.
 It was considered to be on the verge of extinction by 1920.
 A preserved specimen is kept in Tring at the Natural History Museum.
The Beaglier is a designer breed, the offspring of a Beagle and a Cavalier King Charles Spaniel.
 The Beaglier became particularly popular through crossbreeding programs in Australia during the 1990s.
 The dog was developed because of affection for the Cavalier King Charles Spaniel and the Beagle breeds; the breeders were looking for a healthy, energetic small dog with a less active scent drive than that of the Beagle.
 They are very popular in Australia due to their temperaments.
 The Beaglier typically has the shorter and more rounded muzzle of the Cavalier.
 Beagliers have variable coat colours and markings.