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Stratospheric mean residence time  and mean age on the tropopause ΓΩ are shown to measure physically distinct aspects of stratospheric transport. Both ΓΩ and  are mean transit times through the stratosphere of air that enters through tropopause region Ω i and exits through region Ω f, but they represent averages over different populations of fluid elements. The averaging for ΓΩ is based on the population of fluid elements exiting the stratosphere, while  is based on the population of Ω i → Ω f fluid elements residing in the stratosphere. Thus, ΓΩ is the mean age on exit, while is the expected mean residence time in the interior of the stratosphere. The physical basis for defining and robustly computing both timescales is the one-way stratosphere-to-troposphere flux of air labeled with the boundary-propagator Green function, . By re-expressing the boundary-value problem for in terms of first-order loss in a tropopause layer with a timescaleτ c in the limit τ c → 0, we show that both  and ΓΩ can be obtained as ratios of moments of  extrapolated to the tropopause. One obtains  = ΓΩ + 2Δ2/ΓΩ, where Δ quantifies the width of the transit-time distribution. Because the moments of  can be estimated from the mixing ratio of transient trace gases, it is in principle possible to estimate  from measurements of two independent transient tracers. The distinctness of  and ΓΩ is elucidated using idealized models.