Aspergers is on the autistic spectrum, for which the key elements are social communication deficits and repetitive behaviors. Neither one of these are essential elements of giftedness. (In fact, data suggests that GT individuals, on the average, have stronger social communication skills than NT individuals, and are no more prone to repetitive behaviors than those of average intelligence.)
Some of the overlap comes from Aspergers being defined as requiring average to above average intelligence, which tends to enrich the population diagnosed with Aspergers with higher-cognitive individuals, and from the difficulty some NT social groups have in assimilating some GT individuals. It is no more surprising that a GT child whose cognition is comparable to a fifteen-year-old would have difficulty relating socially to five-year-olds than it is that an NT fifteen-year-old would. This is often due to her more sophisticated social skills, rather than impairments.
