As I understand it, TV cook Alton Brown did a good job of explaining Pudding.
Brittish pudding historically referred to a dish that's boiled or steamed, typically in a bag. It could be sweet or savory. Christmas pudding is done that way, then soaked in a brady sauce and lit.
US pudding is more like a custard. Alton Brown would argue that a true pudding has no eggs (as the inventor created the dish for his wife who had many food allergies), and that adding eggs would make it a custard. Jell-O's pudding mixes follow the no-egg theory. My family's recipe for chocolate and vanilla pudding contains eggs, milk, vanilla extract, and chocolate (for the chocolate variety).
My family is also know for taking said pudding, pilling a pie shell with it, and covering with whipped cream.
I have no idea what Yorkshire pudding is, other than it's savory.