Other way around, all Ameraucanas should lay blue eggs. Most Easter-eggers lay blue or green, but some end up not inheriting the blue egg gene and may lay tan or pinkish-brown eggs instead.
Easter-egger is kind of an amorphous term for which different people have different definitions. For example, some don't consider the Legbar-based EEs to be EEs at all, only the Ameraucana-based ones. Some call a pure Ameraucana that does not have the proper coloring a mixed-color Ameraucana, while others strictly state that any non-standard coloring means it's an Easter-egger even if both parents were Ameraucanas. Some say it can only be an Easter-egger if it does have the blue egg gene, and if it does not, then it's just a mix.
The long and short on the Easter-egger name is that it's a catch-all term for a non-standard bird that has the blue egg gene somewhere in its ancestry.