Yes although Ketchup is not really considered to be or sold as a sauce the ketchup is actually a form of sauce because it's made through use of tomatoes that turn into tomato sauce.
So yes ketchup really is a sauce and ketchup is essentially a sauce made with very specifically a sweetened and thickened tomato puree that usually contains vinegar, onions, garlic, and other spices.
So ketchup is basically tomato sauce that has more ingredients such as the spices, garlic, onions, vinegar etc.
The spices can be a recipe that is secret that makes the ketchup taste unique to a certain brand of ketchup such as Heinz.
For example when I buy a cheaper brand of Ketchup it's okay tasting but the Heinz although also ketchup has a better taste to it which is likely because of the secret spices that it probably contains.