It occurred to me that кит is Russian for whale as well, and так means so/thus/in that way in Russian, so someone who didn't know that Russian о often changes to і in Ukrainian could easily misinterpret this sentence as "So, there's a whale there."
Okay, I'll stop being confusing now.
I expect this will be rough for a lot of people. The two forms have different pragmatic force. "The cat's there." is more a general statement of reality or a response to "Where's the cat?". "The cat is there." is usually either for writing or as a way to emphasize that the cat IS there, kind of like Кіт є там.
Yes, they're different.
In 'There is a cat, the 'there' is a pronoun and part of the verb 'is'. It means 'A cat exists' but doesn't say where. It could be 'There is a cat here' or 'There is a cat there'.
In 'The cat is there', the 'there' is an adverb and explains where the cat is. The 'there' refers to the location.