It is not as complicated as I will make it sound. Araucanas and Ameraucanas are specific breeds of chickens. They have very exacting requirements as to what they look like, not just color but many other things, conformation, leg color, comb, tuffs, muffs, skin color, and many other things. These requirements are different in the US than in Europe too, just to make it a little more complicated. These breeds in the US should lay a blue egg, not green. One of the important criteria is that they conform very closely to recognized color and pattern requirements. You can breed two Ameraucanas and if the chick does not match the color and pattern requirements, it is an EE not an Ameraucana. I told you it would sound complicated.
Easter Eggers (EE's) on the other hand, are not a breed, but are considered a type, and I find that misleading. The only requirement is that they have the blue egg gene. They can look like anything, color, pattern, skin color, anything. It really does not matter as long as they have the blue egg gene.
There are several different genes that affect egg shell color. If a hen has the blue egg gene but also some genes for brown eggs, the eggs can come out green. If you look inside a green egg, the basic egg shell is blue, but the hen put a brown coating on it, so it looks green.
Hatcheries do not sell Ameraucanas. They advertise them as Ameraucanas but they are not. They do not conform to the color and pattern requirements so they are really EE's. Most of the hatcheries even say they breed for maximum color variation. If you plan to show them, then this matters. If you are just wanting colorful chickens that lay interesting eggs, EE's are great.