It is well known that chimpanzees are our closest relative as a species: we share at least 98% of our genome with them. Cats have 90% of homologous genes with us and with dogs it is 82% . Two unrelated humans share 99% of their genomes by virtue of being the same species, which means that all humans are 99% genetically similar. The remaining 1% of genes that are different explain the variations in characteristics, such as colour of hair, eyes and skin, and also risk for certain diseases.
When undertaking a paternity test, DNA samples from family members are analysed. By looking at specific DNA markers in each sample, it is possible to identify which half of the child’s DNA is inherited from the mother and which half is from the father. In the case of a biological parent, both child and the parent will share 50% of identical sections of DNA at each marker.
This is where the confusion arises. A chimpanzee shares 98% of our genome, but your own child only 50%? How is that? The 50% figure actually refers to the proportion of DNA that a parent and child share over and above the average proportion of DNA shared by any two unrelated humans. In other words, a paternity test only analyses the percentage of DNA that is identical by descent. This means that a proportion of the child’s DNA is identical to the parent’s DNA – not just because he or she is the same species – but because the DNA came from the parent. However, the parent and child will share more DNA in common over and above this 50%. In other words, a parent and child will share the same 99% that all humans do; and of the remaining 1%, 50% of the DNA will be identical. So, I guess you could say that a parent and child will share 99.5%.
A more in-depth version of this article can be read here.
 Initial sequence and comparative analysis of the cat genome. Genome Res 2007(17):1675–1689.