Pudding cakes are not layered in their construction, rather a mixture designed to separate into 2 separate parts (cake on the top and pudding on the bottom) when baked.
Bread pudding is not layered, rather cubed stale bread mixed with eggs, sugar and milk and baked in a bain marie (water bath). Depending on the cook time and proportion of bread to egg/milk mixture, they can be either quite stiff or quite soft and runny.
The description of a layered dessert made of cake and 'cream' sounds to me like a trifle.
Trifles were very common in the South from the 1700s on. They are originally English and contained fruit and sherry. In the 1700s, Americans began omitting the fruit. They began to be called tipsy pudding (pudding meaning dessert, not Jell-o pudding) in addition to being called trifle because of the alcohol in them.
Hope this helps,
Angel
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