I feel like there is a difference! Please correct me if I am wrong...
Tygrys jest kotem means that The/This tiger is a cat.
Tygrys to kot means that A tiger is a cat (in English we often make it plural (Tigers are cats-- and this is also accepted as a correct answer)
There is construction object + "to" + object (I don't mean the object of the sentence), where "to" means basically "is/are" (though not literally). In this construction both objects are always nominatives.