I'm not sure that that makes them "different"; if I perform an Elmsley Count out to the side, standing on one leg and wearing a red nose does that mean that I could rename it "Dave's Clown Count", because it is performed differently? Surely the mechanics still belong to Elmsley.
You're absolutely right. However, this was 1902, and things were different. For one thing, it's overwhelmingly likely that Erdnase was not aware that this method had been published elsewhere, for a variety of reasons.
Secondly, not everything in Expert was created by Erdnase himself. Many of the methods in the text are either old moves that were well known, even in his day, or moves that were most likely borrowed from already existing texts, or they had been shown to Erdnase by someone else who had read them. It could be that the change in question was shown to Erdnase as a manipulators move, and Erdnase may have simply adapted it.
Expert was not written as a showcase of a man's original sleight of hand, it was written as exactly what it was supposed to be, a "treatise on card manipulation".
It's perfectly likely that either the changes were developed independently. As Erdnase's variation is much more common, and because his book is so well known, it's doubtful you'll get people to change.
Aside from that, Houdini already has enough to his credit. I think we can give the nod to Erdnase on this one.
i still claim houdini and erdnase are the same people
no seriously it seems the evidence does point to houdini but i believe it was created by someone before houdini or erdnase or even at the same time as sometimes happens
I don't know if that's a joke or not.
If you'd like to read up on who Erdnase may REALLY have been, I suggest you read the sections about who Erdnase may have been in "The Annotated Erdnase", as well as "The man who was Erdnase", and Richard Hatch's material on the subject.