Whats going on here is a case of bait and switch. Its true that RNA can transcribe several different DNA sequences and produce the same enzyme.
You're a little backwards here. DNA is transcribed into RNA and RNA is translated into protein.
What you are led to believe is that RNA always transcribes the DNA sequence in exactly the same starting and stopping point everytime and always produces the same enzyme. There is not an exact one to one relation between gene sequence and enzyme produced.
It is true when you are talking about an entire eukaryotic gene, that there is not a 1 to 1 correspondence between gene and enzyme. But that is because of introns that are not translated that are within the gene. Sometimes coding regions will be left out and not translated.
You could think of it this way: A gene could produce a "sentence" of ACAD TYRIN GVQL. It might produce ACAD GVQL or TYRIN GVQL or ACAD TYRIN instead of just ACAD TYRIN GVQL but it can't produce TRACGQVL. The segments can't change, though they can be skipped over or connected with different segments.
What I gave you originally is a coding region, which when translated will always produce the same set of amino acids.
Those different sequences are obtained by different modes of RNA transcriptions over various parts of the whole chromosonal strand.
There are no different "modes" of transcription, but there is different kinds of RNA editing.
Humans and chimps have much identical sequences but those sequences are very specific places for a purpose and God did not have an infinite arrangement of those sequences in order to achieve all shared characteristics between humans and chimps.
As I said, different HUMANS can have have different arrangements of chromosomes and DNA and still appear to be normal. There's no reason that the standard human arrangement and chimpanzee standard arrangement have to be so similar.