Toulouse and Embden are two different -breeds- of the same species. Kind of like crossing a Maine coon cat with a Siamese cat. They're both the same kitty-cat species, but different breeds of it.
As was already said, two species of geese were domesticated by humans --
Anser anser (Graylag goose) and
Anser cygnoides (Swan goose). They are very closely related species, so much so that they can cross-breed, producing fertile young, the way a domestic dog (
Canis domesticus) and coyote (
Canis latrans) can.
A. anser is represented by all of the European (and Euro-American) barnyard breeds -- Toulouse, Embden (Emden), Sebastopol, Roman, Pilgrim, Buff, etc.
A. cygnoides is represented by the Chinese (white Chinese and brown Chinese) goose breed. The so-called "African" goose is thought to be a fertile cross between
A. anser and
A. cygnoides.
By the way, "cygnoides" is Latin for "swan-like." The word should be familiar to anyone who knows swans (The star constellation "Cygnus the Swan" is one hint, and the name for a baby swan -- cygnet -- is another!).
One interesting puzzle, is that the familiar Canada goose (
Branta canadensis) is not even in the genus
Anser like the above geese. It is grouped with the brants. Yet, it is close enough genetically to mate with the
Anser species, but it produces a sterile "mule."