As sourland said, Ameraucana is a specific breed. They lay blue eggs. (So do Araucanas and Cream Legbars and a few other breeds.)
Easter Egger is any chicken that lays blue or green eggs that does not belong to a specific breed. Many of them look like wanna-be Ameraucanas, usually in non-standard colors and often with legs the "wrong" color. It is common for hatcheries and stores to sell them as "Ameraucanas" or "Araucanas," often with a wrong spelling of one of those names.
Having actual Ameraucanas is important if you want to enter them in a show, or if you want to breed genuine Ameraucanas to sell to other people.
Easter Eggers tend to be easier to find, cheaper to buy, and are often better layers than true Ameraucanas. For most people, they are just as good as the true Ameraucanas, and sometimes better. (Many hatcheries do warn that a few will lay brown eggs, which is disappointing if you get one of those few.)