The interaction effect in a two-way ANOVA and moderation in regression analysis are conceptually similar but are used in different contexts depending on the nature of the variables and the analysis goals.

In a two-way ANOVA, the interaction effect examines whether the effect of one independent variable on the dependent variable differs across the levels of another independent variable. In your example, a two-way ANOVA would allow you to test whether the effect of exercise intensity on calories burned is different for males and females. A significant interaction effect would suggest that the relationship between exercise intensity and calories burned depends on gender. Two-way ANOVA is typically used when both independent variables are categorical.

Moderation analysis, often conducted using regression techniques such as the PROCESS Macro in SPSS, examines whether the relationship between an independent variable and a dependent variable is influenced by a third variable (the moderator). If gender is considered a moderator variable, you would include an interaction term (exercise intensity * gender) in your regression model to test for moderation. A significant interaction term would indicate that the relationship between exercise intensity and calories burned differs by gender. Moderation is a broader term that encompasses interactions but is used within a regression framework, which can handle both continuous and categorical variables.

The choice between two-way ANOVA and moderation analysis can depend on several factors, including the type of variables you are working with (categorical or continuous), the theoretical framework guiding your hypothesis, and the specific research questions you aim to answer. If your variables are categorical and you are primarily interested in differences between groups, a two-way ANOVA may be appropriate. If you have a mix of categorical and continuous variables, or if you are interested in the conditional effects of one variable on another, moderation analysis in a regression context would be more suitable.

Go through this.

https://stats.stackexchange.com/questions/18848/moderation-versus-interaction

I think the answer by gung - Reinstate Monica in that StackExchange thread does a good job of explaining what people mean when they talk about moderation. Nevertheless, I really dislike the term moderation as a synonym for interaction. I explain why in the attached PDF. ;-)

Check this link.

https://statisticsbyjim.com/regression/interaction-effects/