Check out the website Ameraucana.org There's the history of the birds coming about and clarifies the differences.
ARAUCANAS = Tufted & Rumpless - Blue Egg gene however the Muffed gene is lethal
AMERAUAUCANA = Bearded, Muffed & Tail - Blue Egg gene & specific colors
EASTER EGGER = Mixed and carry the blue egg gene, colorings varied.
I bought what I thought were Ameraucanas (hatchery) which BYC readers informed me were EEs. They do lay greenish colored eggs and are so very entertaining! One EE lays a darker green/blue egg than the other (although looks white in the first pic), my 2 RIR lay different shades too so I know who lays when. They just started laying, getting 4 a day!!!!