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. I am indebted to Ochef.com for this information.