Sauce – American recipe using ‘a can of tomato sauce’

I can give you the Italian answer - first of all, normally we don't use tomato paste to make sauce, but rather to add a tomato "kick" to recipes. Tomato paste is simply tomato puree that has been cooked down to a high degree of concentration.

A basic tomato sauce is made by

1. making a soffritto with onion, carrot and celery (plus other flavors)
2. adding tomato puree, or "pelati", more rarely fresh tomato
3. cooking the sauce down until the taste and thickness is what you want

If you want to use paste instead of puree, the third step has to be omitted or greatly reduced in duration. Keep in mind that tomato paste has its own taste, and that taste will remain in the final sauce.

In the US at least, common canned tomato products include:

• Paste, cooked down tomatoes, to the point where they are scoopable with a spoon but will not flow. Very thick, like peanut butter. Often sold in six or twelve ounce cans.
• Pureee - cooked tomatoes that have been--well--pureeed, but are mostly at their natural density; also called crushed tomatoes.
• Sauce - cooked down, strained tomatoes, a little thicker than tomato soup. May include herbs, spices, or some flavoring in addition to pure tomato product.
• Diced - solid chopped tomatoes, usually in tomato juice.
• Whole - whole cooked (usually peeled) tomatoes, usually packed in tomato juice. These will still have the seeds.