[Endoperez]

Depends. For one, even if dogs were cats, cats might still be cats. Because of that, you can't say that all non-dogs are non-cats.

If we presumed that the word "cat" would mean a dog, and only a dog, however... A cat would be canus canus, a member of a domesticated species with similarities to wolves. The name with which we call dogs doesn't chance the dogs themselves - the only attribute that would chance is our perception of them, and even in that case it probably wouldn't change besides the name we would call them.