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.