Languages usually mark those differences that the culture they're part of consider important, and downplay or erase those that don't seem that important to the speakers. I would expect the languages of primitive cultures (meaning less technological, less urban, historically ancient, etc.) to mark more, not less, distinctions among animals (but see below), as well as plants, for the simple reason that in primitive cultures the people are (as we would say) "closer to nature", and speakers need to note fine distinctions: different words for animals that can and cannot be eaten, or that can or cannot be dangerous to humans.
I doubt you will find a language used by a primitive culture, in a part of the world where those animals exist, that uses the same word for "dog" and "wolf", because a dog is a hunting companion or a pet while a wolf is a predator and a menace. Now a wolf does look a lot like a big dog, and if someone from a primitive culture who has never seen a wolf before is presented with one, they might use their word for "dog" to refer to it--at first.
Same goes for lions and tigers, which besides their appearance have completely different behaviours: lions live and hunt in prides, coordinating their pursuit of prey, while tigers are solitary --which is rather important to take into account if you're the one being hunted.
All that said, the idea of animal species, families and genera is a late scientific development. Primitive cultures will not group animals based on modern phylogenetic criteria. If two or more species share some salient features they might be lumped together conceptually as one (here I'm thinking of the Old Testament's dietary rules, which are probably older taboos codified as religious law), and this might or might not be visible in their language.
In any case, consider that while our modern languages have a lot of names for different species, most of us would only recognize and consistently use a few of them, and only a handful to refer to animals in our actual vicinity (i. e. not in some NatGeo documentary or someone's travel photo album).