The definition/explanation of the terms/dishes largely depends on the cook...based on his or her family traditions and experiences, as well as regional and sub-regional influences. Often there is lively debate over some ingredients...Does it contain a roux? Does it contain tomatoes, is it thick or is it thin etc.... In the end there is only one rule that is generally agreed upon.....There is no rule....As long as it tastes good.
Etouffee comes from the French meaning...to smother or suffocate...to cook a food in its own juices. (Crayfish, Shrimp, and Catfish would be examples) Small amounts of water or stock can be added, but IMO should be kept to a bare minimum, because the flavor of the food being cooked should be paramount!! (Cook in its own juices) Traditionalists (Count me in that camp) say there is no roux in an Etouffee...If you make a roux; you make a stew...or maybe a fricassee....These same traditionalists say no tomatoes or tomato products...Others disagree and say yes to roux, tomatoes or both!!
I’ve eaten Etouffee with both roux and tomatoes, and even once with a can of cream of mushroom soup thrown in.
They were all good, but to me not a true Etouffee...To me it’s all about the intense flavor of the protein being cooked in its own juices with maybe a little of the protein’s stock/broth added in. I start with butter...1/1/2 to 2 sticks melted in a pan. Then I add 3 or 4 cups of chopped onion, and half again as much bell pepper and celery. Sauté until tender. Season with salt, pepper, cayenne, Creole/Cajun seasoning etc. Add the protein (Crawfish). Cook until the Crawfish is done... just before plating, toss in a little chopped green onion...even less chopped parsley sometimes, and serve on/over rice. No roux. No tomato. Just the intense sweet flavor of the Crawfish "smothered" in the vegetables and seasonings. There is no sauce per se...Only a small amount of liquids that came from the vegetables and the Crawfish --- Cooked properly the butter is the only thickener that’s needed.
Creole Sauce is all together different...Is the basis of many dishes...Is tomato based, sometimes thickened with a little roux. It contains onions, celery, bell pepper, garlic, bay leaves, thyme, etc. It is a “sauce” in which a protein (Shrimp?) can be added, or the protein (Fish?) can be cooked, (broiled, grilled, fried) separately and the Creole sauce served over it on a bed of rice...
Expect to see and hear differing ideas, opinions, and recipes. Remember there are no hard and fast rules. I even ate Shrimp Creole once that contained a cup (at least) of Olives!!! (Italian influence) For what it was.... it was delicious!!! HTH