"Pudding" is an unusual term in that it seems to mean something different in every part of the world. In the US, pudding is a very specific smooth, custard dessert- most commonly associated with the Jell-O Brand and Bill Cosby (are pudding pops still on the market?). In South Africa, 'pudding' tends to be used as a general catchall for desserts; an invitation to a potluck might ask that you bring a salad, drinks, or 'the pudding.' I have no idea what it means to the English, but I imagine it involves some sort of meat and an obscure Anglican holiday.
In Taiwan, like in the US, pudding specifies a specific dessert- only here, it's a formed caramel custard rather similar to flan. It was this kind of pudding that found itself as the flavoring for a milk-box that Bordeaux picked up for me at the minimart. The drink itself was a little unusual, though not as much as I expected. It had a slightly off-putting buttery flavor, but that was outbalanced by the pleasant taste of a creamy caramel.