Question: Are both Bedlington Terrier and Border Collie bred for the same purposes?

Context articles: Border Terrier
Imperforate lacrimal punctum
Teddy Roosevelt Terrier
Border Collie
Texas Heeler
Cumberland Sheepdog
Bedlington Terrier
Paisley Terrier
Collie
Halls Heeler

The Border Terrier is a small, rough-coated breed of dog in the terrier group.
 Bred as a fox and vermin hunter, the Border Terrier shares ancestry with the Dandie Dinmont Terrier and the Bedlington Terrier.
An imperforate lacrimal punctum is a congenital disorder of dogs involving the lack of an opening to the nasolacrimal duct (tear duct) in the conjunctiva.
 Dogs normally have two lacrimal puncta, the superior and inferior.
 This condition can affect either or both.
 Symptoms include excessive tearing and tear staining of the hair around the eye.
 Affected breeds include the American Cocker Spaniel, Bedlington Terrier, Golden Retriever, Poodle, and Samoyed.
 Imperforate lacrimal puncta can be corrected by surgical opening of the punctum.
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 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.
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.
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.
The Bedlington Terrier is a breed of small dog named after the mining town of Bedlington, Northumberland in North East England.
 Originally bred to hunt vermin in mines, the Bedlington Terrier has since been used in dog racing, numerous dog sports, as well as in conformation shows and as a companion dog.
 It is closely related to the Dandie Dinmont Terrier, Whippet and Otterhound.
The Paisley Terrier was a breed of terrier type dog that is now extinct.
 Originating in Scotland, the Paisley Terrier was bred primarily as a pet and showdog version of the Skye Terrier, and was the progenitor of today's Yorkshire Terrier.
 The breed was called the Paisley terrier since most of the dogs came from that location, but it was also called the Clydesdale Terrier, for another location in the Clyde Valley where the dogs were bred.
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.
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.