Tomato paste, or tomato concentrate, consists of tomatoes that have been cooked for several hours, strained and reduced to a thick, rich concentrate. The quality of the tomato paste, of course, depends on the quality of the tomatoes used. It was traditionally made in parts of Sicily Southern Italy and the island of Malta by spreading out tomato sauce that had been reduced by cooking fresh, ripe tomatoes. This sauce was placed on wooden boards which were set outdoors under hot summer sun dry the paste until it was very thick. Tomato paste can be used to enrich the flavor of tomato sauces and other semi-liquids such as soups and stews. Most recipes call for using only a tablespoon at most. The reason is that too much can result in an overpowering tomato flavor or give the sauce too much of an acidic edge.
Tomato puree consists of tomatoes that have been cooked briefly and strained, resulting in a thick liquid. It is a processed food product, usually consisting of only tomatoes, but can also be found with seasonings added. It differs from tomato sauce or tomato paste both in consistency and content; tomato puree generally lacks the additives common to a complete tomato sauce, and does not have the thickness of paste.
Tomato sauce is a somewhat thinner tomato puree. Cooked briefly and reduced slightly, it may include seasonings and other flavorings so that it is ready to be used in other dishes or as a base for other sauces. Tomato sauces are perhaps best known as sauce bases for pasta dishes.