EE are mixes and not a breed. usually will lay a blue, green, pink or brown eggs. Ameraucanas are an APA approved breed and must meet certain standards to be an Ameraucana. Only certain colors and types are acceptable to meet the standards. EE come in all colors. EE can also be Ameraucanas that don't meet the standards, like the color is off are they don't have a beard and muffs. Two pure Ameraucanas that meet the SOP breed together that produce the wrong coloring would then be an EE.
It is clear as mud right? Check out this page
http://www.ameraucana.org/index.html and if your bird is not pictured you have an EE. If you think your bird is there go look at the SOP for that color and make sure. If still in doubt post a pic and ask.....
One more thing EE are usually multi colored not solid, but not always
here is the EE thread with lots of pics
https://www.backyardchickens.com/forum/viewtopic.php?id=273489&p=1
here is the Ameraucana thread with more pics of EE /img/smilies/lau.gif and Ameraucana they will tell you which is which.
When in doubt they are EEs. Lots of people have both, one for variety and one for breeding, both because they are pretty and lay pretty eggs.