Tomato sauce is a condiment made with tomatoes, and sometimes also ham, onions, basil, salt, oil, garlic and various spices. A few tomatoes are broiled, skinned and mixed with a small amount of chopped ham, onion and some salt, oil, basil and other spices. This mixture is boiled and passed through a sieve and a clove of garlic is added, but removed before the sauce is passed through the sieve.
Marinara sauce (from Italian alla marinara 'sailor style') is another term for a simple tomato sauce for pasta made without meat and usually including tomatoes, onions and herbs.
In Australia, New Zealand, and Great Britain the term "tomato sauce" normally refers to the condiment otherwise known as tomato ketchup. In these countries, other sauces made with tomatoes are more usually referred to as pasta sauce etc., depending on their uses.
Source: The Cook's Decameron: A Study In Taste, Containing Over Two Hundred Recipes For Italian Dishes from a project that puts out-of-copyright texts into the public domain. This is from a very old source, and reflects the cooking at the turn of the last century.