I think median is a well defined statistical term but moderator is not a statistical term but rather a scienrific term.

Hi,

to the contrary, mediation is not a statistical concept but a causal concept. A mediator is supposed to transmit the effect of an exposure variable to the outcome. A moderator is a contextual variable on which the occurrence of an causal effect (or statistical relationship, if you broaden the perspective) depends. According to the level of the moderator, the effect can be existent or non-existent or vary with regard to its strength (going from zero to "strong") or vary from negative to positive.

That having said, a mediator can also be a moderator, when the exposure has both a direct and indirect effect (via the mediator) and the mediator moderates the direct effect in its strength.

Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51(6), 1173-1182.

Best,

Holger

https://www.statisticssolutions.com/what-is-the-difference-between-moderation-and-mediation/