Sweetened, this can be a heated thing and I have resisted posted because of it. I am going to give you my opinion (that I of course think is right
) and I know others disagree with me.
Many hatcheries sell birds that they call Araucana/Americana or Ameraucana. These birds rarely meet the Standard of Perfection and don't even always lay a green/blue egg. But because the hatcheries say they are this breed, people sell them on as such.
As you know there are many things that make a breed, a breed, and only one trait of the Ams is the blue eggs. They must also be the right type, have a beard and muff, the right coloured legs and have the right comb. They must also meet the Standard in feather colour. Having said that, there are new colours in development all the time, but these colours breed true. When you breed them together, you know what you are going to get. For example, when I breed one of my Wheaten cockerels to a Wheaten pullet, I know what the chicks are going to look like. These I would call Ameraucana.
This is where it gets tricky and people disagree. If I take my Wheaten rooster and breed him to my Black hen (they are both pure Ams) the resulting chicks will not meet a colour standard. Are they still Ams? I personally don't believe they can be sold as Ams. Just like if you breed a Buff Orp to a Blue Orp, the resulting chicks are not a Standard colour and should not be marketed as Orps.
Back to the hatcheries. The blue egg gene is only needed to be inherited once, as ipf said, to get a green or light blue (if it has no brown egg modifiers) egg. So hatcheries take anything that has one O allele and breeds it to other birds it suspects has an O allele as well. They have no regard for feather colour, or type, or comb. Often these birds have a blade comb instead of a true pea comb.
So my opinion about Ams is if they meet the Standard for type, are a standard colour (or one that is a work in progress) and breed true for it as well as laying a preferably blue egg, then they are an Ameraucana. If they do not meet all of these requirements, they are Easter Eggers. Just because it lays a blue egg, does not make it an Am, just like if it lays a dark egg it does not neccessarily make it a Marans, or a light brown egg does not make it an Orp without meeting other requirements.
There is nothing wrong with Easter Eggers. They are often very pretty birds with a larger body and better constitution than their Am counterparts. And they lay cool coloured eggs.
The Araucanas are much rarer, from my understanding, I have never had them. The ideal has 2 ear tuffs and are rumpless, but as ipf says the tuffting is a lethal gene. They are quite different in type to the Ams, from what I have seen.