What is the difference between a from concentrate and not-from-concentrate product?

The difference is in how the fruit is processed. A not-from-concentrate product means the fruit is squeezed, the juice is pasteurized and then packaged. A from concentrate product means the fruit is squeezed, the water is extracted, which produces a concentrated form similar to that you see in the frozen food department, then at a later time the water is added back and the juice is pasteurized and packaged.