Not really. Americaunas have to be specific colors like Black, Blue, Splash ex. and they also have to follow the breed Standard. Araucanas are different altogether I believe they're tailess, but beyond that I'm not sure. They're all supposed to lay colored eggs ie blue or green. But EEs can lay brown eggs as they're technically mutts.
My hatchery Easter eggers have always been good layers. Not as great as say a sex link or Leghorn, but quite good. Reports on this board have varied widely, though, so Your Mileage May Vary.
Aracauna and Ameraucana both have breed standards, like any other breed. Specific traits and body shape, egg color and plumage color.
EE are a generic, usually wild-type colored bird that are supposed to be bred to lay blue or green eggs. They commonly have beards and muffs, and green or grey/slate legs and pea combs, but these are not 100%.