There are two main types: a boiled then chilled dessert, texturally a custard set with starch, commonly eaten in the U.S., Canada, Germany, Sweden, Poland, and East and South East Asia; and a steamed/baked version, texturally similar to cake, popular in the UK, Ireland, Australia, Germany and New Zealand.
Usually, it is cooked together on the stovetop, but other methods exist including microwaving, steaming, baking (sometimes in a bain-marie), or freezing (using gelatin as a thickener).
Many people make their chocolate puddings at home, but commercially produced tinned or refrigerated versions are commonly available in supermarkets.
In Britain, Ireland, Australia, and New Zealand, chocolate pudding is a dessert made of flour, baking powder, sugar, whole eggs, vanilla aroma, and cocoa powder or chocolate mixed together to make a batter and steamed or baked similar to Christmas pudding.
Texturally it is similar to chocolate cake, but denser courtesy of being steamed or baked with boiling water poured over the pudding batter.