A French Derpy full of Salt

maybe they see us as big monkeys in clothes.

I don't think that dogs think that cats for example are little dogs or small animals like chickens are dogs too... so no. they can see the difference between some species that's for sure.

It's hard to tell whether a non-talking animal understands the idea of "different species", because words are human inventions and "species" is one with such a narrow definition.

I don't think most animals are stupid enough to believe a very different-looking animal actually behaves and communicates the same way they do. They might try to communicate with, say, humans the way they do with each other; the same way we humans speak to animals knowing full well they don't understand our words. Species that were bred to live with humans, especially dogs, actually can interpret our body language and facial expressions; and cats don't typically meow at each other, only at humans.