In (A), the status is current, and continuing. Because it is in the present perfect tense, it is the present state. The progressive element of "been living" implies that it is continuing, currently. In (B), the present perfect tense indicates that the state is current, but not necessarily continuing. It can, in which case (A) and (B) are the same. That is, "it is true that I have lived in New York for 35 years", and incidentally, "it just happens I still am." But (B) can be true even when you no longer live in New York. That is, "it is true that I have lived in New York for 35 years", "but that was 10 years ago, when I moved to London, and I have been here since".

The first one is present continuos, therefore, means that you still lives in NY. The second, means that you is no longer NY citizen.