Based on a lot of research with dogs and how they interact with people it is clear that dogs perceive us as being different to themselves. Dogs change their behavior when interacting with humans. Dogs play with humans in a different way than they do when playing with other dogs.
The photo is Gabriel, my cat in the bushes.
Research on cat behavior, in contrast, has yet to discover changes in cat behavior which suggests that they are interacting with a different animal to themselves except for the obvious fact that we are much larger than them. This last point is important as it can affect behavior and stress levels.
The sort of behaviors that cats do with each other they also do with humans such as greeting with the tail up (friendly), rubbing against our legs, sitting beside us and on us, grooming us and themselves.
There are some slight modifications in behavior such as meowing to us when demanding something which rarely happens between cats as I understand it.
Why do cats see us as cats and dogs see us as being different? It is probably linked to the longer period of domestication of the dog (around 30,000 years some scientists have suggested) compared to the cat (about 9,500 years ago). The cat is only partially domesticated compared to the dog.
If this is correct then in 20,000 years cats will see us as different. That should significantly change their behavior. In the meantime we should learn to meow 😉 . Just kidding. I believe it does help us to understand cat behavior and therefore be better caretakers if cat owners are clear on this.