Psychology Question

I encountered a question about a moderator or a moderating variable, something I had not been exposed to before. I just want to make sure my understanding of a moderating variable is correct. In observational studies we have dependent variable and independent variables and a moderating variable is a separate variable that can enhance or diminish the dv-iv relationship. The difference between a moderating variable and a confounding variable is that a moderating variable we have control over in the sense that different variations of the moderating variable are implicit in the study design. The reason a moderating variable is not considered another independent variable is because it is not the exact relationship we are looking, but rather a relationship that presents itself within the analysis of results. An example would be if we were testing sleep on memory and we noticed that decreased sleep potentially caused decreased recall (experimentally determined), but only in people over the age 40, then the moderating variable would be age.