An interesting point on NPR - there are plenty of human clones walking around right now, and they are being produced at the rate of 30 babies a day in the USA. They are all the 'naturally born' identical twins.
The difference between naturally born twins and cloned twins is that the cloned identical twin would be born many years after it's 'sibling' and would be subject to a very strange set of expectations, and born under very different conditions. This is the crux of the issue behind the Raelian cult's cloning claim.
I was very interested to find out that not only are there the types of twins we have all heard about (fraternal, identical, conjoined), but there also are several other types: mirror, half-identical, and 'twins-of-two.' Google away, folks.