A view on the difference between muffins and cupcakes as depicted by Wauro:
There is a difference between a cupcake and a muffin. Cupcake dough is shitty. Only the icing is good. With a muffin, the dough is awesome even without shitty icing.
When you make cupcakes, but don’t put icing on them, this does not a muffin make. Reason: shitty dough.
Another problem with cupcakes: too much shit on it.
Take that cupcakes!
After having a google, it seems seems that a good distinction between the two is that a muffin can also be a savory, whereas a cupcake is basically a miniature cake, and by definition sweet. A muffin can still be semi-healthy when filled with fruit and nuts, and is therefore more suitable as a breakfast food. The texture of a muffin also differs from a cupcake, it being usually dryer and denser than a cupcake.
Anyone not satisfied with this explanation, feel free to visit sites like this.