What is the difference between a tomato sauce and a ketchup?

Strictly speaking, the dictionaries are correct: Tomato ketchup is a form of tomato sauce, since a sauce is simply "a liquid, semi-solid, or cream food served on other foods".

Difference : 

• Ketchup is most often eaten with pizza, spaghetti, Sandwich, French fries, Burger and hot dogs.
• Sauce is most often eaten with fried foods, meat loaf, and hamburgers.

• Ketchup is cold and is never heated as a rule.
• Sauce is generally served hot.

• Ketchup was prepared with tomatoes, sugar, onions, garlic vinegar/ acetic acid and spices.
• Sauce is made from tomatoes, oil, meat or vegetable stock, and spices. Vinegar is not usually used.

• Ketchup always contains sugar and almost is always thickened, and it contains no lumps or non-blended components.
• Sauce generally does not contain much added sugar or other "sweet spices", and it may or may not be completely blended. The tomatoes may or may not be cooked before blending.