Looking into Russian history, during the fall of the Golden Horde and rise of Moscow, historians seem to always give the label of 'first Tsar of Russia' to Ivan IV, even when the same book will talk about his great grandfather, Vasilii II, using the title domestically, and Ivan the Terrible's grandfather, Ivan II, using the title of Tsar internationally.
Ivan II seems like the candidate most likely to be considered the "First Tsar of Russia." I believe that in a treaty with Lithuania in the early 1500s, he forced them to refer to the Russian ruler as Tsar, though I may be a bit off on that. I know, however, that he started demanding Holy Roman Emperor Maximilian to use the title of "Tsar" to refer to Ivan II. It created a stir, as the Pope first saying that "there is only one emperor, and he does not reside in Moscow" (or something to that extent), and eventually decided that the word Tsar was not too "barbaric" for the Pope to say, and claiming the title of Tsar ranked above king, but below emperor.
And if not Ivan II, then Vasilii III, father of Ivan the Terrible, who had the Holy Roman Emperor finally use the title of Tsar in 1514.
Yet it's only when Ivan IV takes the throne that historians seem to give the Russian ruler the title of "Tsar," even though the title of Tsar had been granted by contemporaries 16 years before his birth, and 33 years before his coronation.
Ivan IV was the first to be crowned Tsar, but not the first to use it. That's the difference. The ones who claimed to be Tsars before him was crowned as the Grand Prince of Moscow, but called them selves Tsars.
So if you would like you could call a couple of other Princes Tsars. But it makes things more simple if you use Ivan IV as the first Tsar because of two reasons: