The effects on social mobility of stratifying pupils into different educational pathways have been debated for decades. We intervene in this debate by showing that stratification in secondary schooling is multidimensional. The extent of "differentiation" into separate tracks is distinct from "hierarchy" between tracks. To address data limitations in existing research, we collect novel data on education policies from 1945 onward for 16 European countries. Combined with mobility data from the European Social Survey, we use difference-in-differences regression models to test the effects of hierarchy and differentiation on intergenerational mobility. Hierarchical stratification shapes the inheritance of educational attainment while differentiation does not. Differentiation only reduces mobility where educational pathways are hierarchically structured. These findings imply that studies using measures of differentiation (e.g., the tracking age) may instead be picking up aspects of hierarchy. They therefore highlight the importance for future research to measure multiple dimensions of stratification and assessing how combinations of policies can reinforce or undermine one another.