Although there is an extensive methodological literature on the measurement of income mobility, there has been little research on the conceptual interpretation of mobility measures and the methodological implications of those interpretations. In this article, I focus on the three measures of mobility that havemost often been used in the literature—the intergenerational elasticity (IGE), the intergenerational correlation (IGC), and the rank-rank slope (RRS)—as well as a recently introduced measure, the intergenerational elasticity of expected income (IGEE). I make three contributions, all related to the conceptual interpretation of mobility measures. First, I specify the formal relationships between those four mobility measures and the measures of inequality of opportunity developed in the luck egalitarian empirical literature on the topic and determine the methodological implications of the analyses. I show that (a) the IGC is a measure of relative inequality of opportunity for monetary income, (b) the RRS is both a measure of relative inequality of opportunity for income rank and a rescaled-by-a-constant measure of absolute inequality of opportunity for income rank, and (c) the products of parental income inequality by the IGEE and IGE are both measures of absolute inequality of opportunity for monetary income that differ in how they measure the value of opportunity sets. Second, I show that an oft-repeated argument, positing that the IGC and RRS are conceptually superior to the IGE because they are not affected by changes in cross-sectional inequality, is based on misinterpreting a mathematical identity without any empirical content as a directed causal relationship and is inconsistent with the results of a formal analysis of the joint dynamics of inequality, the IGE, and the IGC. Lastly, I show that a characterization of the IGE and IGEE as, respectively, “person-weighted” and “dollar-weighted” elasticities is the joint result of a category mistake—equating quantile-specific elasticities to person-specific elasticities—and of misconstruing the nature of the IGE and the epistemic goal it has been meant to serve.