[jraph]

For me, a ketchup is tomato purée / paste + suger + salt + some vinegar + possibly some seasoning (pepper, herbs...). Tomato sauces is a larger category of any kind of tomato based sauce in which we could shoehorn ketchup. A tomato sauce could be purely salted and without any sugar in it, though a pinch of sugar can mitigate the acidic taste.