Just for those who do not know already, the fact is that there is a lot of confusion on the nets, about what exactly the difference is between these three breeds. So, may I offer the following explanation:
Easter Eggers--- a general grouping of chickens that possess the "blue egg" gene. This means that any chicken that is not strictly an ameraucana, an araucana, or some other variety that may lay colored eggs, but does, is an easter egger. Colored eggs may refer to anything from blue, to teal, to olive green, to pink.
Araucana--- First, a little bit of history. The Araucana was created by cross-breeding two local breeds in Chile, South America, creating a chicken breed that in itself has various characteristics. What they created was a breed, that laid blue eggs, could be rump-less (missing last vertebra) or not, and could have ear tufts, or not. In addition the tufted gene, loved by many, and popularized for it's quirky appearance, results in about a quarter of chicks, dying in the egg, a quarter, being without tufts, and half being tufted. This created a lot of discrepancy of what an araucana was exactly, not much of a problem when in a small, isolated environment, but when popularized in modern-day society, created various individual standards of what an araucana is. This resulted in a lot of Easter Eggers, but today they have narrowed it down to down to 2 standards: The North American, and pretty much everyone else.
North American- a chicken breed that lays blue eggs, is rumpless (missing last vertebra), and tail-less, has tufts, and typically yellow skin.
Everyone else- a chicken breed that lays blue eggs, with a rump, a tail, but with beards, muffs, a crest and no ear tufts, along with slate/blue legs and a off-white skin.
Ameraucana- A breed that lays blue eggs, and is a specific grouping of some chickens that would otherwise be labeled easter eggers, that has a standard. They lay blue eggs, have beards and muffs, tail feathers, slate/blue legs, and white skin. One may easily recognize the similarity between Ameraucanas and the non-North American Araucanas, simply the crest is the difference. In reality, other than this small trait, the Ameraucanas are simply the European standard of an Araucana, in America, under a different name.
The biggest piece of advice that I can give is that if you truly want a purebred Ameraucana, or Araucana, do not go to the hatcheries, rather go to a local seller, or breeder, and examine them, if possible with a third party's guidance. If you just want a bird that lays colored eggs, then you should be fine ordering from a hatchery, but as always, purchase local, if possible.