Several alternative mortality models fit Swedish old-age mortality data equally well. The models build on two different concepts of the heterogeneity of individuals in a population. The first concept concerns fixed, genetic differences among individuals in their risk of death. The second concept involves acquired susceptibility to death due to physiological changes and environmental influences. We show that alternative mortality models based on either of these two concepts or some mix of them lead to the same parametric form of observed age-specific death rates. We discuss this duality property of mortality processes and show that even when a mortality model fits the data, the concepts used to construct the model may not be correct.