When a dog bonds to a human, what kind of relationship does the dog think of it as?

Dogs do not see humans as other dogs. They are intelligent enough to realise that we are another species, since dogs mostly communicate with body language that we really can’t mimic. We don’t have tails or snouts, we can’t move our ears and we have half the requisite number of legs. Trying to communicate like a dog will probably only make your dog confused, and also make you look hilarious and you might even end up on a viral video if you’re particularly (un)lucky.

As for what a dog sees a bonded human as, I’d say the closest thing would be a leader. Domesticated dogs have human interaction basically hard-baked into their lives, and dogs have been so bred and conditioned over the centuries that human contact is basically a requisite. As such, dogs quickly learn that humans are a good source of food, shelter and comfort, but they are also the ones who know how the world works, and as such it tends to be a good idea to do what they say. When a dog knows exactly how to react to a given situation thanks to their human they will trust that human more. Alongside providing the dog with food, shelter and comfort, the human will gradually build the dogs’ trust and the bond will be formed.

Dogs do not see us as other dogs, and since there is a species difference there is no concept of being dominant over each other. Dogs should respect and obey their humans, but they will only do so if the trust and the bond is there.