lbaThe American cocktail sauce that I'm used to doesn't have mayo. It's only ketchup and horseradish.
I dunno what Americans you're talking to. The version of cocktail sauce I'm familiar with is ketchup, mayo and horseradish. Pretty much identical to what you've described.
Also, discovered this:
Dr WikipediaIt's more common than I realized. I thought it was only in the states and here.
Cocktail sauce in its simplest form is ketchup mixed with prepared horseradish, though in Australia, the United Kingdom, Ireland, Iceland, France and Belgium, mayonnaise is usually mixed with the ketchup, similar to fry sauce. Furthermore, in Belgium, a dash of whisky is often added to the sauce, and in Iceland, sour cream is considered essential. It is popularly served with steamed shrimp and seafood on the half shell. Many restaurants use chili sauce in place of ketchup. In Australia, it is often provided in fish and chip shops.
In most American oyster bars, cocktail sauce is the standard accompaniment for raw oysters and patrons at an oyster bar expect to be able to mix their own. The standard ingredients (in roughly decreasing proportion) are ketchup, horseradish, hot sauce (Tabasco, Louisiana, or Crystal), Worcestershire sauce, and lemon juice. A soufflÃ© cup is usually set in the middle of the platter of oysters along with a cocktail fork and a lemon slice. Often, the bottles of ketchup and other sauces are grouped together in stations every couple of feet along the counter, but in more sophisticated oyster bars, patrons are served with their own ingredients.