Let me preface this with... I don't know the answer and you should talk to your taxidermist about this.
But...
I have been doing taxidermy for over a decade. Most elk (and any other animal that tends to collect dirt like bears, bulls, goats) do in fact come out of the tan much lighter than when they went in. Its a chemical process not to mention the shampooing and washing the dirt out of the hair.
I didn't see both pictures when I first replied. They do look to be different capes. Could be lighting? Could be that one is cleaner than the other? Could be the first one is wet and appears darker? When the hide was glued to the form it may not have been taxied correctly so the long hair is laying down more than it shouldn which would make it appear shorter? Or it could be two completely different capes.
Sometimes capes get messed up in the process... regardless of who's fault it is, that cape is replaced by another cape (usually someone who only wanted a European mount). If this is the case and the taxidermist did not tell you..well that is not cool.
Sorry a lot of speculation and not really helpful. I'd be curious to see a picture of the mount actually hanging to see how the hair sits...
Most taxidermist mark hides with small holes so they know which customer they belong to when they get them back from the tannery. You could ask your taxidermist if they do this. Maybe it would give you confidence that it is (or isn't) your cape.
Bottom line.. talk to your taxidermist.
Good luck.
Ps. Let us know what they say because now I'm curious.