What is the difference between tomato puree, paste and 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.