Are dogs and cats from the same species?

Dogs and cats are not of the same species.

They are both mammals (class).

They are both carnivores (order).

But different family, genus and species.

Dogs -

Family: Canidae

Genus: Canis

Species: C. lupus, Subspecies: C. l. familiaris

'Canis lupus familiaris' is the domestic dog.

Cats -

Family: Felidae

Genus: Felis

Species: F. catus

'Felis catus' is the the domestic cat.