Handedness is a human behavior where multiple factors work on. It is a complex trait. Basically it based on the comfort and skill. One may be comfortable with right hand where others are comfortable with right. Genetic influence is very less in this case, though very little is known about the biological basis. Hand preference tend to be consistent through out the life and begin to develop during the prenatal stage. Recent studies show that multiple genes can be responsible for the handedness.
DNA sequences can be similar for organisms that are related to each other but through various steps of meiosis like crossing over and law of independent assortment we can get genetic variations that lead to slight differences. We can also get differences in DNA sequences due to mutations.