Question: Are Aidi and Wire Fox Terrier both breeds of dog ?

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Old Jock: Old Jock (1859–1871), was a Fox Terrier famous during the late 19th and early 20th centuries.  A mostly white dog, he ran briefly with a hunting kennel before becoming a show dog, most notably with a victory at the show which popularised the Fox Terrier.  His main show rivalry was with a dog named Tartar, and along with a dog named Trap, the three were popular sires of the Fox Terrier breed.  He was also involved in the early formation of the Jack Russell Terrier and the Dandie Dinmont Terrier breeds.

Signal Circuit of Halleston: Signal Circuit of Halleston was a Wire Fox Terrier and winner of the 1926 Westminster Kennel Club Dog Show.  This was the 50th Westminster show, and the fourth Fox Terrier to win best in show.

Skippy (dog): Skippy (also known as Asta, born 1931 or 1932; retired 1941) was a Wire Fox Terrier dog actor who appeared in dozens of movies during the 1930s.  Skippy is best known for the role of the pet dog "Asta" in the 1934 detective comedy "The Thin Man", starring William Powell and Myrna Loy.  Due to the popularity of the role, Skippy is sometimes credited as Asta in public and in other films.

Canine degenerative myelopathy: Canine degenerative myelopathy, also known as chronic degenerative radiculomyelopathy, is an incurable, progressive disease of the canine spinal cord that is similar in many ways to amyotrophic lateral sclerosis (ALS).  Onset is typically after the age of 7 years and it is seen most frequently in the German shepherd dog, Pembroke Welsh corgi, and boxer dog, though the disorder is strongly associated with a gene mutation in SOD1 that has been found in 43 breeds as of 2008, including the wire fox terrier, Chesapeake Bay retriever, Rhodesian ridgeback, and Cardigan Welsh corgi.  Progressive weakness and incoordination of the rear limbs are often the first signs seen in affected dogs, with progression over time to complete paralysis.  Myelin is an insulating sheath around neurons in the spinal cord.  One proposed cause of degenerative myelopathy is that the immune system attacks this sheath, breaking it down.  This results in a loss of communication between nerves in lower body of the animal and the brain.

Kathleen Pelham-Clinton, Duchess of Newcastle: Kathleen Florence May Pelham-Clinton, Duchess of Newcastle OBE (1872 – 1 June 1955), was a well-known conformation show judge and dog breeder who influenced the Borzoi and Wire Fox Terrier breeds.

Aidi: The Aidi is a Moroccan dog breed used as a livestock guardian, protecting herds of sheep and goats.  It also possesses hunting capabilities and good scenting ability.  In its native Morocco it is often paired in hunting with the Sloughi, which chases down prey that the Aidi has located by scent.

Fox Terrier: Fox Terriers are two different breeds of the terrier dog type: the Smooth Fox Terrier and the Wire Fox Terrier.  Both of these breeds originated in the 19th century from a handful of dogs who are descended from earlier varieties of British terriers, and are related to other modern white terrier breeds.  In addition, a number of breeds have diverged from these two main types of fox terrier and have been recognised separately, including the Jack Russell Terrier, Miniature Fox Terrier and Rat Terrier.  The Wire and Smooth Fox Terriers share similar characteristics, the main differences being in the coat and markings.  They have been successful in conformation shows, more prominently in America than their homeland.

Wire Fox Terrier: The Wire Fox Terrier is a breed of dog, one of many terrier breeds.  It is a fox terrier, and although it bears a resemblance to the smooth fox terrier, they are believed to have been developed separately.

Teddy Roosevelt Terrier: 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.

Caesar (dog): Caesar (1898–1914) was a Wire Fox Terrier owned by King Edward VII.  He was bred in the kennels of Kathleen, Duchess of Newcastle, and became the constant companion of the King.  After the King's death in 1910, the dog attended the funeral and walked in the procession in prominence ahead of nine kings and other heads of state.  Caesar has been the subject of paintings, and a hand crafted hardstone model created by the House of Fabergé.

Supporting paragraphs: Aidi Wire Fox Terrier
Answer: yes