You can’t use “identical” in that sentence because grammatically you must use a noun or a pronoun after an artical “the”. In this situation, same is a pronoun so it is used. “Identical” is only an adjective here, do you understand?
In meaning, identical means similar in every details but same means very the one or thing mentioned to.
Example:
I saw a row of identical houses.
Was that Helen on the phone? => The same. (It means it was Helen).