Twins will start out with identical genetics in the womb. In other words, their DNA will be the same. Random mutation could lead to minute genetic differences between twins, but this is unlikely to have a significant phenotypic impact.
However, environmental factors could cause epigenetic changes which technically results in genetic differences between twins. Epigenetics is a bit too advanced to cover in a simple answer, but read this wikipedia page for an in depth analysis (https://en.wikipedia.org/wiki/Epigenetics).
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