There is no exact dividing line between rich and lean doughs but, in general, rich doughs are those that contain higher proportions of fat, sugar, and sometimes eggs.
Nonsweet breads and rolls, including rich dinner rolls and brioche. These have a high fat content, but their sugar content is low enough to allow them to be served as dinner breads. Brioche dough, made with a high proportion of butter and eggs, is especially rich.
Sweet rolls, including coffee cakes and many breakfast and tea rolls. These have high fat and sugar content and usually contain eggs. They generally have a sweet filling or topping.