A crumpet is a savory/sweet bread snack made from flour and yeast. It is eaten mainly in the United Kingdom and other nations of the Commonwealth.
A muffin is a type of bread that is baked in small portions. Many forms are somewhat like small cakes or cupcakes in shape, although they usually are not as sweet as cupcakes and generally lack frosting. Savory varieties, such as cornbread muffins, also exist. They generally fit in the palm of an adult hand, and are intended to be consumed by an individual in a single sitting.
In Commonwealth countries muffin can also refer to a disk-shaped English muffin. As American-style muffins are also sold in Commonwealth countries, the term muffin can refer to either product, with the context usually making clear which is meant.