Well it starts at when they are conceived. Identical twins come from one egg which is why they have the same genes and DNA and are therefore always the same gender. Where as non-identical twins come from two eggs which is why they have different DNA and therefore look different.
But when it comes to personality that all develops when we are born, therefore every twin in totally unique in this way. Basically this means that even if twins share the same DNA the way they use the DNA as they grow can become very different