There is standard Cyrillic of today.
Earlier versions had a few more characters, and Old Slavonic / Church Slavonic has different vocabulary and verb forms vs. today's Russian. Similar to the differences between Olde English and today's English.
Earlier versions had a few more characters, and Old Slavonic / Church Slavonic has different vocabulary and verb forms vs. today's Russian. Similar to the differences between Olde English and today's English.
I think that you're thinking of the Modern English of Shakespeare's era or Middle English (e.g. 'Whan that Aprill, with his shoures soote'), not Old English (e.g. 'Hwæt we Gar-dena in geardagum, þeodcyninga, þrym gefrunon').
Middle English is very similar to Modern English, and can be read with relative ease. Old English has to be studied as a foreign language.
Note, however, that OCS does not have an ancestral relationship to Russian - it is a Southern Slavic language, most similar to ancestors of today's Bulgarian. Old Russian texts (such as The Tale of Igor) are written in a different language - Old Russian (which existed long before the split into Russian, Ukrainian and so on, so the name "Old East Slavic" is sometimes used).
The comparison to Old English with ash ⟨æ⟩, eth ⟨ð⟩, thorn ⟨þ⟩ and wynn ⟨ƿ⟩ sounds appropriate.