Question: Are the Border Collie and the Smooth Collie both breeds of dog?

Context paragraphs:
Border Collie: The Border Collie is a working and herding dog breed developed in the Anglo-Scottish border region for herding livestock, especially sheep.  It was specifically bred for intelligence and obedience.

Old Hemp: Old Hemp (September 1893 – May 1901) was a stud dog considered to be the progenitor to the Border Collie breed.  He was owned by Adam Telfer, and was used as a working dog to herd sheep.  His style was different from that commonly seen during his era, as he worked far more quietly than the other sheepdogs of the time.  This style was adopted and used by other breeders and trainers and became the most common style among Border Collies within a few generations, with his descendants becoming successful international sheepdog champions.

Halls Heeler: The Halls Heeler was a dog bred by Thomas Simpson Hall to herd cattle on the Hall family's extensive properties in north-western New South Wales in the 19th century.  On "Dartbrook Station", in the Upper Hunter Valley, Hall selectively crossed the offspring of Northumberland Drover's Dogs (Border Collie lineage) that he had imported, with progeny of dingoes that he had tamed.  By 1840 he had bred the type of dog that he needed to control cattle on the massive runs that his family owned, and until he died in 1870 few of these dogs were owned and used by anyone outside the Hall family and their workers.  However the death of Thomas Hall and the break-up of the Hall estate coincided with the development of the dog show, and an interest in breeding dogs to specific criteria or standards.  The Halls Heeler was further developed into two contemporary dog breeds the Australian Cattle Dog and the Australian Stumpy Tail Cattle Dog.  The name is spelled both with the possessive apostrophe, as Hall's Heeler, and without.

Collie: The collie is a distinctive type of herding dog, including many related landraces and standardised breeds.  The type originated in Scotland and Northern England.  The collie is a medium-sized, fairly lightly built dog, with a pointed snout.  Many types have a distinctive white pattern over the shoulders.  Collies are very active and agile, and most types of collies have a very strong herding instinct.  Collie breeds have spread through many parts of the world (especially Australia and North America) and have diversified into many varieties, sometimes with mixture from other dog types.  Some collie breeds have remained as working dogs, used for herding cattle, sheep and other livestock, while others are kept as pets, show dogs or for dog sports, in which they display great agility, stamina and trainability.  While the AKC has a breed they call "Collie", in fact collie dogs are a distinctive type of herding dog including many related landraces and formal breeds.  There are usually major distinctions between show dogs and those bred for herding trials or dog sports.  They typically display great agility, stamina and trainability and more importantly sagacity.

Footrot Flats: The Dog's Tale: Footrot Flats: The Dog's Tale (stylised on posters and titles as Footrot Flats: The Dog's Tail Tale) is a 1986 New Zealand-Australian animated comedy film based on cartoonist Murray Ball's comic strip "Footrot Flats" about a New Zealand farmer and his border collie sheepdog.  The film was written by Ball and Tom Scott, directed by Ball, and produced by John Barnett and Pat Cox, with music by Dave Dobbyn.  The voice cast includes leading New Zealand actors John Clarke, Peter Rowley, Rawiri Paratene, Fiona Samuel and Billy T. James.  It was New Zealand's first feature-length animated film.  The film was released on 9 April 1986 by Kerridge-Odeon.  "Footrot Flats: The Dog's Tale" grossed $2,500,000 at the New Zealand box office (making it one of the most successful local films of the 1980s).

Ashleigh and Pudsey: Ashleigh and Pudsey is a British dog trick act, comprising trainer Ashleigh Jade Butler (born 7 February 1995) and Pudsey.  Pudsey (28 December 2005 – 20 July 2017) was a male Border Collie, Bichon Frise, and Chinese Crested powderpuff cross.  They first achieved prominence as contestants in the sixth series of the television talent show "Britain's Got Talent", which they won on 12 May 2012, becoming the first ever dog trick act to win the competition.

Cumberland Sheepdog: The Cumberland sheepdog is an extinct dog breed related to the border collie and other old working collie types.  It is claimed to be one of the ancestors of the Australian shepherd and in the early part of the 20th century some Cumberland sheepdogs were being referred to as border collies and may have been absorbed into the latter breed.

Smooth Collie: The Smooth Collie is a breed of dog developed originally for herding.  It is a short-coated version of the Rough Collie of Lassie fame.  Some breed organisations consider the smooth-coat and rough-coat dogs to be variations of the same breed.

Scotch Collie: The Scotch Collie is a landrace breed of dog which originated from the highland regions of Scotland.  The breed consisted of both the long-haired (now known as Rough) Collie and the short-haired (now known as Smooth) Collie.  It is generally believed to have descended from a variety of ancient herding dogs, some dating back to the Roman occupation, which may have included Roman Cattle Dogs, Native Celtic Dogs and Viking Herding Spitzes.  Other ancestors include the Gordon and Irish Setters.

Texas Heeler: The Texas Heeler is a crossbred herding dog found mainly in Texas.  They are a cross between the Australian Cattle Dog, and the Australian Shepherd, but can be a cross between the ACD and the Border Collie.  They are bred mainly for their ability to work cattle.  Found mainly on ranches in the past, they are currently being enjoyed in dog sports such as agility, frisbee and Rally Obedience.

Supporting paragraphs: Border Collie Smooth Collie
Answer: yes