The development of a truly identical twins versus mirror image twins comes down to timing. A single sperm will fertilize a single egg and begins development by splitting into more cells. If this group of cells, now called blastocyst splits into two separate parts in the first 9-12 days, identical twins will be born. But if the split occurs after that, they will be mirror-images of each other.
Fraternal twins are an entirely different matter. Fraternal twins are no more identical than any other sibling pair and are the result of two separate sperm fertilizing two separate eggs. This is can occur naturally, the result of the mother releasing more than one egg at ovulation. It may also be the result of medical intervention as many women take fertility drugs to improve their chances of conception. There is also a hereditary link as the incidence of fraternal twins do occur more often within a family.
Many people have seen the popular American television show CSI (Crime Scene Investigators) and may recall the episode with the Chimera, a man who had two sets of DNA. This phenomenon occurs when the blastocysts of developing fraternal twins fuse, resulting in a single individual with two sets of DNA. This condition usually results in a fully functional individual and is not detected unless a clear abnormality prompts testing. Though it has been considered a rare condition, it is found to be more common than originally thought in a variety of animals, including humans. And the condition is more common among children conceived through in vitro fertilization than naturally.
By the way, you can read about the amazing birth of identical quadruplets from my hometown, Calgary, Canada here.