A central theme in ecological research is to understand how species interactions contribute to community dynamics. Species interactions are the basis of parametric (model-driven) and nonparametric (model-free) approaches in theoretical and empirical work. However, despite their different interpretations across these approaches, these measures have occasionally been used interchangeably, limiting our opportunity to use their differences to gain new insights about ecological systems. Here, we revisit two of the most used measures across these approaches— species interactions measured as constant direct effects (typically used in parametric approaches) and local aggregated effects (typically used in nonparametric approaches). We show two fundamental properties of species interactions that cannot be revealed without bridging these definitions. First, we show that the local aggregated intraspecific effect summarizes all potential pathways through which one species impacts itself, which are likely to be negative even without any constant direct self-regulation mechanism. This property has implications for the long-held debate on how communities can be stabilized when little evidence of self-regulation has been found among higher-trophic species. Second, we show that a local aggregated interspecific effect between two species is correlated with the constant direct interspecific effect if and only if the population dynamics do not have any higher-order direct effects. This other property provides a rigorous methodology to detect direct higher-order effects in the field and experimental data. Overall, our findings illustrate a practical route to gain further insights about non-equilibrium ecological dynamics and species interactions.