This is the way I understand it:
Blue-egg-laying birds were imported to the U.S. from flocks in South America. These birds were not very well standardized, they had a variety of different physical traits and characteristics. The people who bred blue-egg-laying chickens disagreed about what these birds "should" look like and eventually split up into three different groups:
1) People who thought it would be best to eliminate the tufts and rumplessness, because these genes made propagation more difficult. People who bred these birds eventually had them standardized as Ameraucanas (which I believe is short for "American Araucana"). They determined that their birds should have muffs/beards, tails, and white skin.
2) People who thought the tufts and rumplessness should be preserved. People who bred these birds eventually had them standardized as Araucanas (after the region of Chile where the first rumpless and/or tufted birds were discovered). They determined that their birds should have tufts, NO muffs or beard, be rumpless, and have yellow skin.
3) People who thought the traits didn't matter so much as long as the birds laid colored eggs. These are today's Easter Eggers, which cannot be standardized because their traits vary so widely. They can have any plumage color, any comb type, any skin or leg color, may or may not lay blue or green eggs, most though not all are tailed, many have muffs/beards but others don't, etc.
Hope this helps somewhat.