The presence of various mechanisms of non-genetic inheritance is one of the main problems for current evolutionary theory according to several critics. Sufficient empirical and conceptual reasons exist to take this claim seriously, but there is little consensus on the implications of multiple inheritance systems for evolutionary processes. Here we use the Price Equation as a starting point for a discussion of the differences between four recently proposed categories of inheritance systems; genetic, epigenetic, behavioral and symbolic. Specifically, we address how the components of the Price Equation encompass different non-genetic systems of inheritance in an attempt to clarify how the different systems are conceptually related. We conclude that the four classes of inheritance systems do not form distinct clusters with respect to their effect on the rate and direction of phenotypic change from one generation to the next in the absence or presence of selection. Instead, our analyses suggest that different inheritance systems can share features that are conceptually very similar, but that their implications for adaptive evolution nevertheless differ substantially as a result of differences in their ability to couple selection and inheritance.