At first glance, it may seem that the difference between muffins and cake lies purely in their size. After all, cakes tend to be fairly large while muffins typically fit in your hand. This theory crumbles when cupcakes are added to the mix; they are small cakes that look strikingly similar to muffins. There are, however, several notable and striking differences between cakes and muffins.
Muffin batter and cake batter are fundamentally different. A typical muffin recipe contains about half as much fat and sugar, proportionally, as a typical cake recipe, though exact amounts vary. In general, though, a muffin recipe might include 2 tbsp. sugar and 1/8 cup fat per cup of flour, while a typical cake recipe would contain closer to 4 tbsp. sugar and 1/4 cup fat per cup of flour. Cakes also typically contain more eggs.
In many cases, you can tell cupcakes apart from muffins simply by taking a look at them. Cupcakes tend to be frosted, while muffins are bare. This difference extends to large cakes as well, which also tend to be frosted. Muffins, on the other hand, frequently contain flavorful additions such as fruit or nuts. Cake may be fruit- or nut-flavored, but will generally not contain actual pieces of these items the way many muffins do. Except in the case of cupcakes, cakes tend to be larger and flatter than muffins, which are relatively small and have peaked tops.
Despite their similarities in ingredients, you do not make muffins and cupcakes in quite the same way. Bakers generally make cakes by creaming the fat and sugar together then adding the other ingredients (though this method works for muffins too). On the other hand, the classic muffin method involves combining all the wet ingredients, then combining all the dry ingredients, then mixing the two together. Cakes may include yeast, which muffins do not.
Cakes and muffins function dramatically differently in society. Thanks in part, perhaps, to their lower fat content relative to cakes, muffins are a perfectly acceptable breakfast food and are a common accompaniment to a morning coffee. Cakes, on the other hand, tend to be a dessert item. There are, however, a few exceptions to these rules; a chocolate muffin studded with chocolate chips may serve as dessert while coffee cake can be a breakfast food.