The sauce that Sankalan has defined is used as a topping or a gravy. They are prepared in the kitchen – just the way we sauté or prepare our masalas – onions, ginger, garlic, chilli, turmeric, coriander, salt and spices - for our gravies. There is no hard and fast rule of what goes into these sauces. Every dish requires a different set of ingredients. White sauce, for instance, is just flour, butter and milk and seasoning. The ingredients depend on what is being cooked.
Bolognese sauce used in Italian cuisine uses beef, pork rinds and some herbs and tomatoes. You make a sauce with bell peppers and tomatoes and it goes on top of traditional pizza bases.
The question about the sauce and ketchup referred in the post appear to be about the bottled versions that we can buy in the market.
Of course, now different variations of tomato sauce/tomato ketchup are introduced, but traditionally, these two are the same – different regions, different names.
“You painted a naked woman because you enjoyed looking at her, put a mirror in her hand and you called the painting “Vanity,” thus morally condemning the woman whose nakedness you had depicted for your own pleasure.” - John Berger