From what I understand many of the pie doughs of the period were the same thing as pudding dough, everyone had a pot to boil stuff in and it was just extra if you had an oven and pie pans, sometimes with noted cooking times for a pan at the end. The that era of American cooking kind of blends puddings and pies so that they mean basically the same thing. Similar someone making a pan fried rice recipe today and just adding on the end of the recipe if you are fancy and own an actual wok you can adjust cooking times for that.
From what I understand many of the pie doughs of the period were the same thing as pudding dough, everyone had a pot to boil stuff in and it was just extra if you had an oven and pie pans, sometimes with noted cooking times for a pan at the end. The that era of American cooking kind of blends puddings and pies so that they mean basically the same thing. Similar someone making a pan fried rice recipe today and just adding on the end of the recipe if you are fancy and own an actual wok you can adjust cooking times for that.