Fitness and natural selection are often treated as though they refer to the same phenomenon. APS distinguishes them because they address different aspects of evolutionary continuity.
Fitness concerns the differential continuity of persistence-sustaining organisation across generations. Living systems differ in their capacity to contribute to future continuity under particular developmental and ecological conditions. Fitness identifies these differences in continuity.
Natural selection concerns the differential historical stabilisation of those differences. Selection does not create fitness, nor does fitness create selection. Rather, selection operates upon historically existing differences in continuity among forms of organised persistence.
The relationship can be understood as a sequence. Organised persistence generates differences in continuity. These differences constitute differences in fitness. Natural selection then differentially stabilises those differences through evolutionary time, contributing to the historical transformation of persistence-sustaining organisation.