Ketchup is tomato sauce. However, people use these two words differently.
For instance, customers in a restaurant would ask a waiter, “Can I have some ketchup.” The word, Ketchup implies that the sauce is ready to use.
In the other hand, people use the word, Tomato Sauce as a part of the dishes’ name such as Tomato Sauce with Shrimp, Tomato Sauce with Chicken.