When it comes to sauce and ketchup, we usually think the same but actually, they are not. If we talk about food historians ketchup is a sauce, the word sauce is originated from Latin word salsas which means ‘salted’. With the commercialization and experimentation, the sauce is now a very household thing and many people make different types of sauces at home. 

Whereas, tomato sauce is made from tomatoes, oil, meat or vegetable stock and spices. It never uses vinegar. Also, ketchup is cold in nature and is never served hot, while all varieties of sauces are served hot.

origin
Ketchup word arose from Chinese koechiap meaning ‘brine of fish’, or generally mentioned as ‘spicy sauce’; the word sauce is originated from Latin word salsas that mean ‘salted’. Ketchup is originally supposed to have been invented in the seventeenth century and was related to a sauce that contained fish brine, herbs, and spices as main ingredients.
Key differences

Ketchup is made with tomatoes, sugar, vinegar/acetic acid and spices. Whereas, tomato sauce is made from tomatoes, oil, meat or vegetable stock, spices and never uses vinegar. Also, ketchup is cold in nature and is never served hot, while all varieties of sauces are served hot.
 

Verdict
Ketchup is a sauce but not all sauces are Ketchup. Ketchup is what you have as a condiment while sauces can also be thin gravies.