All dogs can still interbreed, so they're still the same species. They're different enough from wolves that they're given a different sub-species, sort of like Homo Sapiens Sapiens and Homo Sapiens Neanderthalensis. However, the variety within domesticated dogs is similar to race.

What makes dogs breeds so different is that the dog genome is extremely plastic: it has a lot of room for variation as evidenced by how far pugs have come from wolves, even though theoretically they can still mate and produce fertile offspring.