What is the difference between Tomato Puree and Tomato paste?

The Tomato Puree and Paste differ by the amount of Natural Tomato Soluble Solids (NTSS). The USDA specifies that tomato puree must contain 8% to 23.9% NTSS, the paste must contain minimum of 24% NTSS.

The commercial packers crush ripened red tomatoes; strain out skins, seeds, and other non-soluble solids. The evaporators are used to reduce moisture under vacuum. Under vacuum, the liquids boil at 135 to 145º F. This helps to preserve the tomato flavors.  At home, if one would reduce the liquids, they would boil, and then simmer for a long time. Both the high boiling temperature (212º F) and long cooking time contribute to loss of flavor.

Unfortunately, the packers are not required to label the products with more information. You might have to read the ingredients very carefully. Some packers will give you the specific gravity. Specific gravity is a measure of weight. For example, one cup of tomato juice of 1.025 specific gravity weighs 2.5% more than one cup of water. 2.17% NTSS contribute to 1% increase in weight of water. 

Three commonly sold Purees are as follows:

Medium, 10% NTSS, 1.045 Specific Gravity

Heavy, 13% NTSS, 1.06 Specific Gravity

Extra Heavy, 15% NTSS, 1.7 Specific Gravity

To make curries at home, I recommend using Medium or Heavy Tomato purees. They will save time to clean, as well as vacuum controlled moisture reduction gives good flavor.