Relatedness between individuals as well as evolutionary relationships between populations can be studied by comparing genotypic similarities between individuals. When hypervariable loci are used to describe genotypes, it is shown that both of these problems can be approached with a unified theory based on allele sharing between individuals. The distributions of the number of shared alleles between individuals indicate their kin relationships. Extending this, we obtain statistics for genetic distances between populations based on average number of alleles shared between individuals within and between two different populations. Traditional statistical inferential procedure can be used to establish specific kinship relationships between individuals. We derive estimates of the number of hypervariable loci needed for a specified reliability of such an inference. Evolutionary dynamics of genetic distance statistics based on allele sharing is also studied. It shows that such measures of genetic distances remain linear with the time of divergence for a period comparable to that of the gene frequency-based measures of genetic distances. Statistical properties of measures based on allele sharing establish that for using such summary statistics it is not necessary to know the full characteristics of all loci used. It is enough to know the degree of heterozygosity per locus and the number of loci. Therefore, in principle, this approach can also be used for DNA fingerprinting data in the studies of relatedness between individuals as well as between populations. The possible compromising features of multilocus DNA fingerprinting data are also discussed.