The classic American dessert known as pudding is a sweetened milk mixture thickened with cornstarch, then cooked. It has no eggs in it, and is also known as blancmange in fancy cooking terminology. (The term pudding is used widely for other foods, but we’ll save blood pudding, Yorkshire pudding, bread pudding, and steamed pudding for another time.)
Custard is pudding’s eggy cousin. The New Food Lover’s Companion defines custard as a dessert made with a sweetened mixture of milk and eggs that can be either baked or stirred using gentle heat. According to the more technical explanation in Le Cordon Bleu’s Professional Baking manual, custard is “a liquid thickened or set by the coagulation of egg protein.” Crème brûlée is a custard, for example.
But it’s not quite as simple as saying, “If it has eggs it’s custard; if it has starch it’s pudding.” Professional Baking points out that there is an overlap: Cream puddings, it says, use a custard base but are thickened with starch. Pastry cream (the stuff you find in an éclair) is a cream pudding—a custard-pudding hybrid.