This paper provides a thorough comparison of causal models used in causal mediation analysis for identifying mediation effects, focusing particularly on separable effect method. Separable effects, proposed by James Robins, are claimed identifiable without the need for the untestable cross-world assumption implied by the nonparametric structural model with independent errors. However, our study clarifies that separable effects do not guarantee a mediation interpretation due to violation of a mediation null criteria. This paper reveals that when the separable effects provide mediation interpretation, they are the same as the natural effects, but rely on assumptions stronger than the cross-world assumption. Furthermore, when there is a mediator-outcome confounder affected by exposure, separable effects do not have a mediation interpretation, while another study has shown that the natural effects and interventional effects have a mediation interpretation under a no conditional mean causal interaction assumption. Our study elucidates the relationship between separable, natural, and interventional effects and proposes an integrated framework that is applicable to practical analysis of clinical studies. We emphasize the key role of the untestable isolation assumptions in separable effects for mediation interpretation, and highlight a trade-off between the interpretability and falsifiability of assumptions.