Question: Are both American Foxhound and Löwchen types of Foxhounds?

Context:
Treeing Walker Coonhound
The Treeing Walker Coonhound is a breed of hound descended from the English and American Foxhounds.
 The breed originated in the United States when a dog known as "Tennessee Lead", was crossed into the Walker Hound in the 19th century.
 The Treeing Walker Coonhound was recognized officially as a breed by the United Kennel Club in 1945 and by the American Kennel Club in 2012.
American Foxhound
The American Foxhound is a breed of dog that is a cousin of the English Foxhound.
 They are scent hounds, bred to hunt foxes by scent.
List of foxhound packs of the United Kingdom
The following is a list of foxhound packs, recognized by the Masters of Foxhounds Association, in the United Kingdom who would formerly have hunted foxes, but are now obliged to undertake alternatives-either trail hunting or legal fox control methods- due to limitations imposed by legislation (excluding Northern Ireland).
English Foxhound
The English Foxhound is one of the four foxhound breeds of dog.
 It is a cousin of the American Foxhound.
 They are scent hounds, bred to hunt foxes by scent.
Dumfriesshire Hound
Dumfriesshire Black and Tan Foxhounds were a pack of foxhounds kennelled at Glenholm Kennels, Kettleholm, near Lockerbie until they were disbanded in 2001.
 They were established by Sir John Buchanan Jardine, author of "Hounds of the World" (1937), after the First World War.
 The hounds are believed to have originally been created by crossing Bloodhound/Gascony blue/English Foxhound.
 They were larger than standard foxhounds and were black and tan.
 Although that pack was disbanded in 1986, there is a pack descended from them in France, known as Equipage de la Roirie.
Foxhound
A foxhound is a type of large hunting hound bred for strong hunting instincts, great energy, and, like all scent hounds, a keen sense of smell.
 In fox hunting, the foxhound's namesake, packs of foxhounds track quarry, followed—usually on horseback—by the hunters, sometimes for several miles at a stretch; moreover, foxhounds also sometimes guard sheep and houses.
Löwchen
The Löwchen or Little Lion Dog (German: "Löwchen" "little lion," French: "Petit chien lion," "little lion dog") "is a breed of dog.
 A small dog, they are considered by some registries as a toy dog and by the American Kennel Club as a non-sporting dog."
Black and Tan Virginia Foxhound
The Black and Tan Virginia Foxhound is an American foxhound breed.
 It resulted of a cross breed with Bloodhounds in the 1700s.
 The breed was developed by the landed gentry in order to get a dog suitable for fox hunting.
 Besides the Black and Tan there are the Walker, Calhoun, Penn-Marydel, Goodman, July and Trigg, which all developed from similar crosses.
 The Black and Tan is believed to descend form hunting dogs imported to America by Robert Brooke in 1650.
 These hunting dogs were the ancestors of several varieties of American hounds and stayed with the Brooke family for more than 300 years.
 Afterwards French Foxhounds were bred in after George Washington received them as gifts from the Marquis de Lafayette.
 Much later, the breed's speed and stamina were improved introducing Irish Foxhounds.
Trigg Hound
The Trigg Hound (also known as the Trigg Foxhound or Hayden Trigg Hound) is a variety of the American Foxhound, developed in Kentucky by Colonel Haiden Trigg.
International Foxhound Association
The International Foxhound Association (IFA) is incorporated in France as a NGO since 2012.
 The purpose of IFA is the promotion of the English Foxhound as a breed.
 The members of this association are masters of recognized packs of foxhounds from France, Germany, Italy, Belgium, Portugal, Canada, Australia and New Zealand.
 IFA represents members outside countries with existing Master of Foxhound Associations (MFHA).
 The director of the MFHA in the UK is committee member of IFA.
 The association publishes its own studbook of a selected number of the best packs of foxhounds in the World and organizes yearly hound shows at Chateau de Selore in France.
 Baroness Monique de Rothschild, Patron of IFA, and, Baron von Pfetten, President of IFA published an article in covertside magazine on the "history of the English foxhound".

Answer: no