Of course what a cat _is_ to me is not what a cat _is_ to you, because we necessarily have different memories of interactions with cat-like beings. If you show some babies a cat for the first time, they'll necessarily see it from different viewing perspectives. Even if you put VR glasses on them and show the exact same video, they'll have different contexts: "I first saw a cat when I was sitting next to my friend", "I first saw a cat when I was thinking of ice cream", etc.

But they all saw the same cat, they'll see many other cats, who are all similar. So everyone will understand that "things like these are cats", but everyone will have their own understanding of a "cat" because their memory is different.