Many people think that the DNA of identical twins is very similar, but not identical. This is incorrect, however - identical twins generally DO have identical DNA. The reasoning (borne out by genetic testing, of course) is as follows.
In almost all cases, what happens is that a fertilised egg splits into two masses early on in fetal development - each of which develops into a fetus. Thus their genes are 100% replicas of each other, at least initially.
There are rare causes of identical twins not having the same DNA - such as when a new mutation occurs in one twin after the split. But this is real fine print stuff, and not really worth considering here.
However, twins do NOT have identical fingerprints. Fingerprints are partly genetically inherited, but there is a substantial environmental contribution that takes place in the womb. These factors include things like nutrition, blood pressure, position in the womb, and position of the fetus. These vary from twin to twin, giving each similar, but not identical, fingerprints.
Therefore, identical twins have the same DNA, but not the same fingerprints.