Muffins are a kind of sweet treats, very common in Anglo-Saxon countries. Originally spelled moofin, a word probably coming from ancient German muffen, indicating a small cake.
Cupcakes are small, single-dose cakes, originally baked in small cups, from which the name, first mentioned in American cookery, by Amelia Simmons.
Both of them can be prepared both sweet or savory versions.
For size and cooking method, Muffin and Cupcakes are quite similar with each other. The main difference is that Cupcakes are made just alike the regular cakes, whereas in order to make Muffins, you should gather all the dried ingredients in a bowl, and the fresh ones in another one, and then you can combine them all. Besides that, Muffin are eaten plain, whilst Cupcakes are usually decorated with some icing.
Anyway, whether you prefer Muffins or rather Cupcakes, you will definitely get soft and flavored tasty morsels.