Dog categories

[S7ENN]

Into either of whcih two categories do all dogs belong/

[garner]

Canine and or Vulpine.

[Lie-in King]

...and Lupine?

[wildwood]

If you mean the domestic dog, they are all Canis lupus familiaris species.
For all the dog-like (foxes, wolves, coyotes, jackals etc.) animals to fall in the same category you have to track back to the Family category which is Canidea

The full taxonomic name for the domestic dog is......
Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Carnivora
Family: Canidae
Genus: Canis
Species: C. lupus
Subspecies: C. l. familiaris