These days, I'd say not much! Vespawoolf is correct that muffins are intended to be a quick bread, whereas cupcakes are mini cake desserts, usually with frosting or glaze.
However, bakeries are making muffins so decadent these days with tons of added sugar and other items (like chocolate chips, etc.), one cannot necessarily say that a muffin is any "healthier" than a cupcake!
We like making our own muffins from scratch, rather than purchasing them from a bakery or baking them from a mix. Any bread recipe (pumpkin, banana, etc.) can be made into muffins. Generally, the baking time is about 1/3 less than for an entire loaf.