Sake classifications are influenced two factors: milling and brewing ingredients.
The milling process concerns how much of the rice grain is actually used in the brewing process. The more the rice is milled (ie. the closer to the core of the rice grain is), the higher the quality of the sake. There are three milling ratings, four if you count non-milled grains as well.
Then there are the brewing ingredients, of which there are very few. The « pure rice » classification (« junmai » in Japanese) consists of sake that has nothing more than the simple ingredients of rice, water, yeast and koji (the mold used in fermentation). There are no additives whatsoever. On the other hand, there is the « alcohol-added » classification (« aruten » in Japanese) which consists of sake brewed with the exact same ingredients as « pure rice » but then adds a distilled brewers alcohol to the sake mash. Adding alcohol affects the body, aroma and viscosity. All of this leads to two types of ingredient ratings.
The two classifications together offer a guide to sake.
Junmai Daiginjo (50% or less of the rice rain remaining), Junmai Ginjo (60% or less), Junmai (70% or less, or no milling)
Daiginjo (50% or less of the rice rain remaining), Ginjo (60% or less), Honjozo (70% or less), and Futsu-shu (no milling).
Thus within their respective classifications, Junmai Daiginjo and Daiginjo are the premium sakes, and thus the most expensive. They will be bolder, robust and full-bodied.