Let me help. This is wikipedia.
The definitions of tomato purée vary between regions. In the USA, tomato purée is a processed food product, usually consisting of only tomatoes, but can also be found in pre-seasoned form. It differs from tomato sauce or tomato paste in consistency and content; tomato puree generally lacks the additives common to a complete tomato sauce, and does not have the thicknesss of paste.
To prepare tomato purée, ripe tomatoes are washed and the leaves and stem are removed. Some processors remove the skin of the tomato as well. This is then mashed or mechanically chopped to the desired consistency.
Tomato purée can be used in soups, stews, sauces, or any other dish where the tomato flavor is desired, but not the texture. It is often deprecated by professional chefs, who find it to have an overly cooked flavor compared to other forms of canned tomatoes. This is sometimes a non-issue, as in long-cooked dishes, but in quick sauces such as a marinara sauce it is undesirable.
Tomato purée is sometimes referred to by its Italian name, passata di pomodoro, when it has been "passed" through a sieve to remove seeds and lumps. In this form, it is generally sold in bottles or aseptic packaging, and is most common in Europe.
In the United Kingdom, 'tomato purée' usually refers to what in America is known as concentrated tomato paste. In the UK passata refers to sieved uncooked tomatoes.
This is the Italian wikipedia (googled and arranged by your truly)
Concentrato: obtained at different levels of concentration of tomato juice (solid content ranging between 12% and 36%)
Pelati: Tomatoes of long type to which the skin is removed and is usually added tomato juice half concentrated
Passata: it is tomato juice partially concentrated with a solids content between 7% and 12%
Polpa: it is made from tomatoes that are peeled and diced, through a process called "live", as the freshly picked tomatoes are processed.
Personally, I recognize the Italian wikipedia. None of the above are sauces, but ingredients for cooking. After some elaboration, they can become sauces. Like I take an onion, I chop it and cook it to transparency in oil, I add a can of pelati, let it simmer till it looses most of the liquid and I have an excellent tomato sauce, as such.
Or I am in hurry. I take a spoon full of concentrato, add 3 to 5 parts of water, microwave it, and I have a basic tomato something to add to whatever I have to add to. If I use it to season some pasta, they fire me as cook and I have to start all over by cleaning the rest rooms.
Like beautiful J**** (beautiful is not enough for this gorgeous Quebequaise that broke more than one heart in this part of the world) who came to visit for a couple of days and stayed for six months, and how nice it was to eat in 3 at the table instead of just the 2 of us that after 10 years we had started to know each other a bit too much, and one day she made herself a pasta and seasoned it with ketchup right out of the bottle and when I looked at her with wide eyes, and gaping mouth, she just smiled and everything was perfectly ok. Ah, the tomatoes. Who cares, beauty wins them all.