What's the difference between a cupcake and a muffin?
There is considerable overlap between cupcakes and muffins.

Method

From a technical point of view, muffins are made by the muffin method, making them small quickbreads.  In the muffin method, the wet ingredients are combined in one bowl; and the dry ingredients are combined in another bowl.  Then the two are quickly incorporated together with minimal mixing to avoid gluten development.  This gives muffins a somewhat coarse crumb.

Cupcakes are small cakes, and are made by one of the traditional cake methods such as the creaming method, the reverse creaming method, the genoise method, the chiffon method, and so on.  They tend to have a finer crumb than muffins.

Contrast

While no single criterion distinguishes a muffin from a cupcake if you do not adopt the technical definition above, the following trends exist:


Cupcakes tend to be sweeter than muffins; there are savory muffins such as cornbread
Cupcakes are often iced or frosted, whereas muffins tend to have no topping, or a simple crumb topping
Cupcakes usually have a head or top no larger than the body of the cupcake; muffins are often encouraged to overflow their baking cup, so that their top is larger in diameter, giving them somewhat of a mushroom shape
Cupcakes are almost always, well, cupcake shaped; muffins can be made as just muffin tops
Cupcakes are almost never crispy or crunchy; muffins are often encouraged to brown and develop texture, especially on the tops