Strata Vs. Bread Pudding: What's The Difference? - Tasting Table

Bread pudding is a custard-like bake made from stale bread soaked in a mix of milk, eggs, sugar, and vanilla. The mixture is baked until the liquid ingredients are set and turn golden brown. Depending on where you're from or what recipe you use (like this Irish bread and butter pudding recipe), other ingredients such as walnuts, spices, and raisins can be added.

O&H Danish Bakery cites bread pudding's origins as English, appearing sometime in the 12th century, but the dish was not as delicious as it is today. It was considered "poor man's pudding" until milk and eggs were added into 13th-century recipes; the baked treat was then cleverly renamed "bread and butter pudding." 

Since stale bread is traditionally the base of this recipe, experimenting with different kinds of bread can lend unique textures and flavors to the dish. Many bakers like to use brioche because it is sweet and soft — characteristics that can help create a delicious morning treat or afternoon snack (via St. Pierre Bakery).