How can stuff be sweeter than sugar?

When a new artificial sweetener comes out, it is invariably described as being several hundred time sweeter than sugar. Is this because sugar forms crystals and so is not distributed well over the tastebuds, or is it that a given molecule of Nutrasweet stimulates the taste buds more somehow?

The latter. It’s measurement of how sweet something tastes relative to the amount of substance provided. Sugar crystals dissolve in saliva, and in any case would probably be provided in solution anyway in taste tests, so that has nothing to do with it.

There’s not even one such entity as “sugar.” What we commonly refer to as “sugar” is really Sucrose, one of the hundreds of different types of sugars all of which have different levels of sweetness.

As the commonest, the sweetness of Sucrose is used as a reference point of 1.0 when measuring sweetness. Fructose is the sweetest common sugar at 1.73 (or 73% sweeter than sucrose). Glucose is 0.74; Maltose and Galactose are 0.32; Lactose is 0.16.