For most amino acids, there are several DNA triplets that code for it (there are 64 triplets and only 20 amino acids). Even if there is one magical optimized protein that the species converges to, there is no evolutionary pressure for the triplets to be the same in the two converged genes.
This is an important point. DNA is an ECC. And it seems the distribution of triplets to amino acids is not random, but has converged on a mapping that maximizes the robustness of the organism. Pretty darn amazing.
