A chile relleno is a Big Jim pepper stuffed with asadero cheese, battered and fried. Full stop.
Sometimes, in places that are not New Mexico, a waiter will put a plate in front of you. You will look down and see what appears to be an omelet, wrapped around an anaheim or pasilla or poblano pepper with a little cheese thrown on top.
You may ask, “What is this?”
If the response is, “A chile relleno,” then you have encountered a liar and you have great cause for sadness.
Mouthful of Feathers 
True.
Not so!
There is a long history of authentic and tasty Tex-Mex rellenos made from poblanos stuffed with more than just cheese. The New Mexican skinny Big Jim versions are limited in scope, though admittedly nice in a burrito.
Finally!!!
I can’t believe it took so long for someone to come and argue this point. I should have known it would be a New Mexican who decided to pursue this!
Let’s put aside the pepper choice for a moment. Do you condone an omelet wrap as opposed to an egg batter?