What is the difference between tomato puree, paste and sauce? I was looking for a recipe for an Italian tomato sauce when I came across an old cookbook from an American Creole Chef I like, but I'm really confused about the terminology he uses for some of the ingredients and wondered if someone could clarify exactly what he's referring to.

In the recipe he asks for -


2 cans (6 ounces) of tomato paste
2 cans (10 3/4 ounces) of tomato sauce 
2 cans (10 3/4 ounces) of tomato puree


I've always assumed that tomato paste and tomato puree were the same thing, but clearly not. Can anyone clarify the difference between these two?

Tomato sauce in the UK comes out of a ketchup bottle, is he referring to passata, sieved tomatoes? If not, what is he referring to?
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.