Tomato concentrate and tomato paste are synonymous... the only
difference is in degree of concentration (water content), ie. the
product in tubes is more concentrated than in cans but otherwise it's
the exact same product... even among different brands of canned tomato
paste concentration differs, so in reconstituting to make tomato juice
how much water to add is strictly a matter of personal taste. Orange
juice concentrate is made pretty much by the same process, as are all
fruit juice concentrates; water is removed with relatively low heat to
prevent cooking and vacuum. Fruit juices are concentrted as a form of
preservation and to reduce shipping costs by reducing weight/bulk.
When buying tomato juice one pays more, for the reconstituting, the
large container, and higher warehousing and shipping costs. This
topic has been discussed here a few times over the years only drawfs
have very short memories (to match their stature) so here is a
refresher course:
http://www.fruitjuiceconcentrate.org/tomato-paste