Tomato paste, or tomato concentrate, consists of tomatoes that have been cooked for several hours, strained and reduced to a thick, rich concentrate. It is generally fairly sweet.
Tomato puree consists of tomatoes that have been cooked briefly and strained, resulting in a thick liquid.
Tomato sauce is a somewhat thinner tomato puree, and may include seasonings and other flavorings so that it is ready to be used in other dishes or as a base for other sauces.
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Found the above on the net for you!
Where I live tomato paste is cheap, but sauce, puree, tomato juice, etc. are really expensive. I always just buy the paste and add water, a little for puree, more for sauce, and even more for juice! I haven't had any problems interchanging like this.
Katy