The games were the same. Even the name remained unchanged. The word shatranj has no independet meaning in Arabic, it's just a phonetic adaption of the Sanskrit chaturanga (the fourpartite).
Back then, there was no official body to codify the rules and there were certainly variants at various places and at various times. We also don't know how the game was played in India; it's only reasonable to assume that the rules were the same.
As an example, some Arab manuscripts seem to indicate a double move of the rook and centre pawns to allow a quicker development of the elephants. But we don't know how widespread such variants were.
Hello,
I'm interrested in the history of chess and I was looking for the oldest known variants. Apparently the oldest one is Chaturanga which became Shatranj when it was adopted by the arabs and later Chess. But I have a hard time figuring out the difference between Chaturanga and Shatranj. It seems that the rules are the same (same moves but different names for the pieces). Does someone has an answer ?