I believe it's in the coloring, it goes into the difference at the beginning of this thread. Ameraucanas will breed true, that I know. And EEs will throw some wacky, odd,and splendid colors. EEs are my favorite, of the three.
Michigan, that one EE of yours looks like a cross between some kind of an EE (bright green legs is sure give away) and either a Welsummer or Brown Leghorn. I'd be interested in knowing what kind of egg you get from her.
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I have not read the entire thread so maybe this has already been said, but the EEs with a pea comb are more apt to lay the greenish/blue eggs. Single and rose combs, or others seem to lay the brown, pink and white eggs.
I love EEs and bought them as Ameraucana when I first got chickens, and learned early on that they were in fact, not going to win any prizes at the fairs.
I am keeping my EEs because I love the surprise aspect and I love the coloring. I make up my own names for their colors, like blue laced buff or black laced brown.
My thinking is it IS important so that people know what they are buying. Many folks buy the EEs thinking their kids can show them at the fairs and since they are mutts, are disappointed, or are disappointed by the eggs being any color other than blue.
It is more than just about spelling. Advertising EEs as Ameraucanas or Araucanas, gives the impression of being an inexperienced seller and one I won't buy any stock from. Same with Marans and other breeds.
Here are the newest arrivals at HenHaven! Two EEs and 2 BOs. I have enough brown chickens, so I went with Buffs and the lightest colored EEs in the batch that had puffy cheeks! Any guesses as to how the one with the dark markings will turn out?