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A Stardust Box is a box which contains, as the item explains, Stardust. Each Stardust Box tier has a different chance to get a Shooting Star:

Stardust Box

Chance

Stardust Box I 1/2,000
Stardust Box II 1/500
Stardust Box III 1/50

With the Medium Brewing Achievement perk, the Shooting Star drop rate of each box is doubled.