in my studies some (maybe trivial...?) questions on interaction/moderation in probit/logit regression came up. Imagine the following setting (to be analysed with probit/logit):

dependent variable D (discrete)

independent variable IN

variable V

hypothesis I: IN has a negative effect on D.

hypothesis II: if V is high, IN's effect on D is not so strong.

First of all, I get confused on what is the difference between interaction and moderation? As I see it, in technical terms, these are all about "interaction"?

Now, when I analyse hypII, what do I include in the model? I would include IN and IN*V to explain D. Do I need to include V as a separate variable? If so, why?

Without V as a separate variable, regression shows significant results. When I include V as a separate variable, the independent variables are not significant anymore. What does the imply?

When I apply this logic to a different dependent variable, is there a difference between probit/logit and OLS?

Thank you very much in advance.

Kind regards

Ute