The concept of tortillas being wrapped, filled and eaten in various forms was clearly defined by the Aztecs. There does not seem to be any reference to the term "enchilada" that dates back to the Aztecs. The first reference to the term "enchilada" in the U.S. came in 1885.
According to Dictionary of American Food and Drink an article in "American Speech" in 1949 described the enchilada as "a Mexican dish prepared more for turista than for local consumption".1
"The word “enchilada” simply means “in chile” and in Mexico, the most beloved version is actually a street snack: a corn tortilla dipped in chile sauce that’s a far cry from the limp, stuffed tortillas swimming in a sea of red sauce and molten cheese that we’re familiar with in the U.S. Rick shows us how to make classic “Street Style” Red Chile Enchiladas at home, and how to transform them into a simple, satisfying brunch presentation, Red Chile Enchiladas with Spicy Potatoes and Fried Eggs. At Sanborn’s in Mexico City, the colorfully tiled restaurant where the famous dish, Enchiladas Suizas, was invented, Rick explains that “Suiza” means Swiss, a tribute to the dish’s use of cream and cheese."2
Andrew F Smith (Oxford Food Companion To American Food and Drink credits the Centennial Buckeye Cook Book from 1876 assembled by the woman of the First Congregational Church located in Marysville, Ohio.3
Diana Kennedy (author of Art of Mexican Cooking) explains that there are two basic methods of making enchiladas.4
In the U.S. the most common enchilada is filled, rolled, then topped with sauce and frequently cheese.
The other method, less common in the U.S. is the stacked enchilada. Tortillas are lightly fried, placed on a serving plate, then the ingredients are placed on top of the flat tortilla. Typically this will be repeated at least 3 times. This style of enchilada is most common to Sonora, Mexico and in the Southwestern part of the U.S.
Today enchiladas are commonly filled with cheese, chicken, beef, pork and onions. Early recipes from the 19th century suggested very simple fillings such as onions onions and olives seasoned with salt and Mexican oregano. Cheese was not typically used as a filling but was commonly used as a topping. Other early fillings included picadillo, or mixtures of ground pork, olives and flavored with chiles, oregano and cumin.5
A red chile sauce made from rehydrated dried chiles and (sometimes) tomatoes and seasonings is the most widely used enchilada sauce. There are even cream based sauces like that used for Enchiladas Suizas, and some enchiladas are topped with a traditional mole sauce.