Wellllll.........
It *does* make a difference what you call things. For instance, this forum is called the Backyard Chickens Forum. If somebody selling chickens decided to set up their own web site and called IT the Backyard Chickens Forum, the owners of the original BYC would have every reason to be upset. Identity matters.
In the case of the whole Araucana/Ameraucana/EE thing, I think it's very unfortunate that the two breed clubs picked such similar names. It just adds to the confusion. But it's still worthwhile to let people know about the differences between the birds, because they ARE different. A rumpless, tufted bird is NOT the same thing as a tailed, bearded, muffed bird. If we *call* them the same things, then they are robbed of their individual identities.
In my mind, EEs are more or less equivalent to production Reds. EEs are sort of the production version of Ameraucanas. So I don't waste much energy correcting people there. And I would certainly not be rude to the neighbor with the birds, but in the course of talking to him I might say something about how much things have changed with these breeds over the years, and that we now have them separated into Araucanas and Ameraucanas -- and then explain the recognized differences. It could be a good learning experience for both of you!