It’s an interesting discussion; how dogs and cats perceive us. It appears that dogs perceive us as different to themselves while cats do not. We can judge this by the way they interact with us. There’s been a lot of research on dogs (far more than the research on cats by the way) on how they interact with people.
It’s become clear that dogs know that we are different to them. When they see a human being they change their behaviour. And the way they play with people is different to the way they play with other dogs.
The same cannot be said about domestic cats. It appears that when they are fully socialised to us and are therefore friendly with us they interact with people as if they’re interacting with other cats. For example, on the basis that they are friendly towards us they will greet us with their tail up which is a known friendly greeting in domestic cats. They also want to nose touch which is also a friendly greeting but unfortunately we are too tall.
They often rub against our legs which is another friendly greeting and the process of scent exchange. They deposit their scent on us and they receive our sent which goes on their fur. This is reassuring to them. Also, they lick us; they groom us as if they are grooming another cat. In the cat world this is called allogrooming or mutual grooming. It helps to create a bond between cats and of course it certainly helps to create a bond between cat and person.
The point being made is that the domestic cat does not distinguish us from other cats which points to the possibility that they see us as a large cat. The size difference is an issue for me. Domestic cats are probably more anxious, more often than people realise. One reason for this I would argue is that they are living with a very large companion creature namely a human. If we lived with a friendly being that was 10 times as tall as us you would have to be incredibly trusting to not feel intimidated.