Yeah Moscow sometimes referred to as Third Rome by people who view it as the continuation. The Holy Roman Empire would have of course differed as the Kaiser (also Caesar derived) similarly counted himself as the continuation of the Roman Empire.

And since when Tsar is Byzantine title? :)))

Tsar is a contraction of Caesar as pronounced in Slavic languages. The corresponding Byzantine title was Basileus, and while the word itself is unrelated, the title correspondence was very well established at the time (much like the use of "emperor" for Chinese and Japanese rulers, even though the titles in those languages are not etymologically related, either).