Sorry you lost your girl.
Actually, they are very much related. The Araucana was first developed in Chile from two other breeds. The original Araucanas included both a tufted and rumpless variety and a bearded muffed tailed variety. In the 1920s the blue egg laying birds were introduced to the rest of the world via a paper. Both varieties were introduced into the US and different breeders focused on devolving the two separate types. The hatcheries were more interested in making money from the craze because of false information being perpetuated that the blue eggs were healthier. Not caring about standards, they crossed the birds with other breeds and created the Easter Egger.
In 1976 the APA accepted only the tufted and rumpless variety as Araucanas, though many wanted both varieties accepted. This of course left the breeders of the bearded muffed tailed variety upset. They, however, continued to show their birds as "American Araucanas." Meanwhile, a club of such breeders worked together on establishing their birds as a separate breed. They were the ones to establish, via voting, the breed standards and the name Ameraucana (see what they did there). This breed was accepted by the ABA in 1980.
Interesting side note, a ship wreck landed a bunch of bearded muffed tailed Araucanas in Scotland early on. Their offspring produced some of the tufted and rumpless birds. That is why Britain and Australia accept both verities as Araucana.
Sorry that was probably more then you wanted to know.