As another 'Murican, the way I understand it is that if it’s boiled or steamed inside of an animal intestine or stomach, that’s a pudding. And even if it’s fried later, it’s still a pudding. See: Black Pudding, a British blood pudding.

And if it’s only steamed, often wrapped in a cloth, it’s probably a desert.

In any case, if some British person offers you a “pudding” don’t ask questions you really don’t want the answer to. Just shut up and eat it. They ARE British after all. And if you really don’t want to risk it, ask if you can go to a curry shop instead. Blessed be the Indians who taught the Brits to cook at least one edible dish.