No, the scientific name for British Shorthair is British Shorthair, and "blue" is just one of its coat colors. Many people call British Shorthairs "blue cats" because the most common coat color for British Shorthairs is a large, all-blue face. However, strictly speaking, "blue British Shorthair" is not a breed, just a coat color. British Shorthairs and blue cats are not the same breed. British Shorthairs also come in a wide variety of coat colors, such as blue and white, golden and silver shaded, and tabby. 
Blue cats aren't exclusive to British Shorthairs; the Russian Blue, for example, is also a solid-colored blue cat. It belongs to the same breed as the Russian Blue and is one of the oldest cat breeds in the world. Originating in Port-Angelo, Russia, it is affectionately known as the Angel Blue. The Russian Blue once faced extinction, so breeders crossed it with Siamese cats to preserve the breed. Today's Russian Blue is more similar in size to the Siamese, while retaining the blue color of its ancestors.
In the domestic market, cats with blue fur are generally called blue cats. However, the British Shorthair Blue is just a color variant of the British Shorthair, while the Russian Blue is a breed recognized by the British Shorthair Cat Association.
