When cloning was first talked about the idea was that you would take a cell and create a copy of the original animal.
Cloning as achieved in "Dolly" and other animals used the cell nucleus of an adult cell and put it in an egg cell from another animal and grew that. As a result the "copy" is not exact.
Link to full articleThey used induced pluripotent skin cells, or iPS cells -- cells that have been reprogrammed to look and act like embryonic stem cells. Embryonic stem cells, taken from days-old embryos, have the power to morph into any cell type and, in mice, can be implanted into a mother's womb to create living mouse pups.