Your right Avatar Twins are a good case.
Natures own version of cloning, a person who before birth, splits.
So you end up with two people of near identical genetics.
The only reason why there is any difference between the two people is just because there are two of them, and they get named differently.
This causes a whole number of changes that wouldn't occur with one person. Like friends that one has and the other doesn't, or differences in schooling or work (since if there was one position only one could fill it forcing the other to be somewhere else)
Most of the time twins tend to try and show they are an individual and try to be different from one another.
As for clones... Well here is something:
If I cloned you today, what age you are now you would have to add onto it for it to be the same as you are now. (So if your 18, you'll be 36 by the time it is 18)
So a clone although would have the same genetics as a person, wouldn't be of the same age. In fact they will suffer aging far worse, for instance your sample was taken at age 18, that means that there is a high chance that the clone will grow with 18 year old cells, so it's life expectancy will be 18 years less.
(of course thats if it was a 100% clone, but cloning has to use a few building blocks thrown in. Like for instance an Embryeo from a donor, which can change the genetics overall.)
There is also the other point, that Men and women are have a majority of genetics derived from their mothers. (afterall a man leaves a little sample, and the woman has to put up with the consequences for months, allowing her physiology to help build the offspring. So although you have genetics shared by your mother and father and their bloodline, your predominantly a part of your mum.