Actually, I think you have it backwars. The same sequences can result in many different kinds of proteins. Not only that, we now know that genes are not the beads on a string sequences that the geneticists once supposed them to be. DNA is read forward and backward, on the sense and anti-sense strands, and even between multiple chormosomes and then spliced together. It is obvious that it is the cell controlling this process, and not the genes themselves. If you interested, I have some fascinating (creationist) links on the subject—GGG
Here's a link which suggests that I don't have it backwards:
The table in the section titled "Degeneracy of the Amino Acid Code" suggests that there are only two amino acids which have unique codons. The others have multiple codings.
My question is whether the genetic information for presumably related species shows a tendency for identical proteins to be coded identically, despite the fact that there would be multiple codings possible.