Two ways to slower aging - or just one?

In the context of teaching relativity, one encounters two situations in which two observers age at different rates. Usually, these effects are treated as if they were independent of each other. Often one is referred to as special-relativistic, the other as general-relativistic. We show that both are special cases of an effect which follows naturally from the fact that space and time form a unity. They exist in a flat space-time and therefore neither of them deserves the label general relativistic.