Americans are sometimes confused by how Brits use the word “pudding.” In the UK, “pudding” basically just means dessert, so anything sweet could be a pudding. For example, what Americans call pudding (something kind of similar to a blancmange) would be a pudding, so it is possible to have an American pudding for your pudding.
But you would never have a Yorkshire pudding for your pudding, because a Yorkshire pudding isn’t sweet after all, unless it is used to make a Dutch 
No one would have a Black Pudding for pudding, though, because it is blood sausage, and I don’t think anyone would have a Suet Pudding for pudding, either, as I can’t imagine anyone ever eating a Suet Pudding for any reason sort of imminent starvation. American’s might choose a Steak and Kidney pudding before opting for a Suet Pudding, but not by much.
You might be excused for thinking a Christmas Pudding is a Black Pudding, but they are two different things. A Christmas Pudding is dark in colour but sweet, in a way that some people might find tempting to try.