Shta is the clearest case in the alphabet of a single sign that means different things in different countries, and the divergence is not a corruption of one by the other. Both are regular outcomes of the same inherited material.
In Bulgarian the letter is read as the cluster sht, which is what it was named for and what Old Church Slavonic had. Bulgarian is the modern language closest to the recorded Slavonic here, and its letter name is still built on the sound.
In Russian the same letter writes a long soft sh, historically the cluster shch, and Russian names the letter accordingly. The difference goes back to a divergence in how the inherited consonant groups developed in the south Slavic and the east Slavic areas, a divergence older than any of the modern national languages.
Two consequences follow. The first is practical: a Slavonic word read aloud in Sofia and in Moscow will differ audibly at exactly this letter, which is one of the reasons the pronunciation of Church Slavonic is not uniform across the Orthodox world. The second is evidential: because the divergence is regular, the treatment of this letter in a manuscript is a piece of information about where the manuscript was written, and Slavists use it that way.
A shared alphabet conceals differences of this kind rather than removing them, which is a general property of writing systems and a specific reason to be careful about reading a Slavonic text aloud in one national tradition and calling it the original.