"This is a cat."
Translation:To jest kot.
That could be very specific circumstance- you point out to the specific person/animal and claim this one is the/a cat. Maybe you have litter of house cats and wildcats , and you point one and say' ten jest kotem", "a ten jest żbikiem".
"this is" usually translates to "to jest" These are usually translates to "to są", regardless of the gender of the noun.
also,"to in this sentence, and in the "noun is noun" sentences, makes grammar simpler, you use nominative after to.
To is a difficult concept in Polish, because it can have several meanings depending on context.
In this case, to is not a demonstrative pronoun, but a genderless dummy pronoun (part 2. in the link), which is used in constructions like "This is X".
Ten, on the other hand, is a pure demonstrative pronoun. I believe that whenever you can replace "this" with "it" in English, you can't use a Polish demonstrative pronoun, but only to.
It "to" is in "this is" sentences, then no "to" is always "to". also "noun is noun" sentences. ( To here never changes and the nouns stay in nominative case)
If it's the cat=this cat/that cat then yes it's ten kot (this cat, masculine word), ta kotka (this female cat-feminine word), to kociątko (this kitten, neuter word).
To here changes with gender, number and case. wiktonary