Actually 'Domestic Long-Hair' isn't a breed, it's a catch-all term for any domestic cat of unknown breed with long hair.

American Shorthair (which is a breed) was originally known as the Domestic Shorthair, the breed was renamed "American Shorthair" in 1966 to better represent its "All American" character and to differentiate it from any other shorthaired breed.

'Domestic shorthair' now is a catch-all term for any domestic cat of unknown breed with short hair.