The answers we get depend largely on the questions we ask. Seems simple enough, yet why is it we're always surprised with those answers?
I remember asking the kids if they did their homework. They'd answer yes or no honestly until the realized my question was general enough to tell the technical truth without violating the honesty rule. After all, I didn't ask if they did all their homework. Nor did I ask if they did it well.
It reminds me of digital audio. I continually get the same question about bits. "If bits are bits how can those same bits sound different?" Good question because, on the face of it, if the bits are identical then they must sound identical. Only, we're not really asking if the bits are identical. Are we? No, in fact, what we're asking when we approach the subject of 'bit perfect' is the veracity of the bits from only one angle, when there are many.
Had we asked if the timing of the bits were identical we might get a different answer. Or the rise time of the bits, or the spacing between one another. Or when we ask why a 'lossless' file sounds different than a raw file, despite the fact we can prove the bits are 'identical'.
But no, when we ask if it's 'bit for bit' perfect what we really are asking is for an exact count of 1's and 0's and if they're in the right order. And the answer to that is typically yes. But that question and that answer do not even scratch the surface of what we're really asking.
The correct question is "why do they sound different?"