Well, they look the same to me. But here is what wikipedia says about them.

A crumpet ( krʌmpɪt (help·info)) is a savoury/sweet bread snack made from flour and yeast. It is eaten mainly in the United Kingdom, but also in the other nations of the Commonwealth.
http://en.wikipedia.org/wiki/Crumpet

A muffin (US: English muffin), also known as a hot muffin, or a breakfast muffin, is a round, yeast-leavened form of bread almost always dusted with cornmeal. It may be eaten at breakfast in North America and Australia, but may be served as an afternoon meal in England.
http://en.wikipedia.org/wiki/Muffin_(English)

It looks like a crumpet has a sweetness to it while an English Muffin is just bread.

Maybe other PTers with some actual experience with both can enlighten us.