The term Bombay cat is used to refer to two different breeds of cat.
British Bombay Rectify
The British Bombay cat is the name given to Black cats of the Asian group. It is a cat of Burmese (cat) type with a black coat, toes, nose, and Copper (color) to Greenish eyes. Can also be seen as a Tabby with dark charcoal grey and light grey striped when you lift up the fur is a grey underneath.
American Bombay Rectify
The American breed called Bombay was created in 1958 in Louisville, Kentucky, when Nikki Horner of Shawnee Cattery deliberately bred an American Shorthair with a Burmese for the purpose of creating a domesticated cat that resembled a wild panther (also known as baby panther). The offspring of this breeding did indeed resemble the black Leopard of India. The name came from the Indian city of Bombay (now Mumbai). Horner called her creation the "patent leather kid with the new penny eyes."
The Bombay is a muscular yet agile cat with a black coat. The heads of Bombay cats are rounded and wide with a short tapered muzzle. The eyes, which are of golden or copper color, are rounded and set wide, and their ears are broad, slightly rounded and medium sized and, like the eyes, set wide. The Bombay has a coat that is short, satiny and tight to the body. Bombay cats do not require grooming.