Which sentence is correct?

The cat’s tail. This cat owns her own tail and that is why there is an apostrophe and an ‘s’. If that wasn’t there then that would mean there was more than one cat. If you know the cat is called Ginny, then you’d write ‘Ginny’s tail’. If you don’t know the name you use the noun to describe it - like cat. You have to make sure that the cat still owns its tail by showing possession through the apostrophe.