Yes jmburns,when you add horseradish you are now working on a creole sauce that is great with po'boy sandwiches and that brings us back to fried foods.
Ironic or not, American Sauce is a description used in Europe, typically in UK. As Petitbleu correctly noted Sauce Américaine is a classic French sauce invented in Paris by a chef who earned the nickname "Chicago" because he had worked in kitchens there. But in common parlance (again in UK) it usually refers to a mixture of ketchup and mayo with a bit of mustard. Which makes more sense with fried food like corn dogs or frites.
In the case of this French Poodle recipe, Sauce American is just ketchup. But the recipe also recommends providing mustard, on the side, for the dish.
http://food52.com/recipes/12338-french-poodles
Sauce Américaine is a classical French sauce made with lobster shells, onions, garlic, tomatoes, fish stock, etc. It's fairly complicated, as most of those French sauces are. However, I'm not sure if this is what you're talking about. Could you be more specific with your question?
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http://food52.com/recipes/12338-french-poodles