Using DNA testing technology, we can determine whether twins are fraternal or identical.
In fraternal twinning, two different eggs (ova) are fertilised by two sperm to produce two genetically distinct children, which share the same genetic relationship as siblings born at different times (full siblings). The twins could be male or female, there is no bias.
In identical twinning, a fertilised egg (an ovum) splits into two and then the two embryos develop independently. The two babies have the same original genomes (a carefully chosen phrase).
For fraternal twins we expect to see a different DNA profile from each other (but still be able to statistically calculate the relationship) and for identical twins, we expect to see the same (identical) DNA profile.
For general curiosity testing, this type of test is sufficient to resolve any question of fraternal vs identical.