As for the differences, I won't go into it in detail because there are LONG threads on here on the subject already, but here is the brief summary:
Araucana: extremely rare breed, totally rumpless with TUFTS (not muffs or beards) and lay BLUE eggs only. They also carry a lethal gene connected to the tufting gene which makes them hard to breed successfully. These come ONLY from breeders and are very hard to find. Hatcheries do NOT have them, but they often label their EEs as such.
Ameraucana: also rare, tailed, muffed, and bearded only available from breeders, not ever from hatcheries, though they are again often mislabeling EEs as Ameraucanas. These birds conform to very specific color requirements and any bird that is tailed, muffed, and bearded but is a different color cannot be considered an Ameraucana and then by default is generally called an Easter Egger. Ameraucanas lay blue eggs (and maybe green as well... I have heard debate on this and I am not an expert).
Easter Egger: a bird of mixed heritage that generally carries the blue egg gene. They are usually tailed, muffed, and bearded and because of their mixed heritage can sometimes be missing one or more of those traits and also they lay eggs in a rainbow of colors... ranging from light blue or green to bright blue, blue-green, olive green, bright green, lavender, pink, brown, and sometimes even gold. These are the birds you will get from hatcheries and feed stores and are very hardy, fun-loving, and great layers. Wonderful birds for the backyard if you don't plan to show.
