Question about deciding whether something is a moderator or covariate Based on what I know, a moderation analysis is simply looking at an interaction between an IV and a moderator. However, people often refer to moderators when they talk about ANCOVA (analysis of covariance). In this situation though, one of the assumptions of ANCOVA is that there is no interaction between the IV and the covariate.
Why use the term moderator in reference to ANCOVA? And how does one decide if something is a covariate or a moderator? For example, if I am looking at whether a diversity intervention impacts bias scores and I am interested in whether trait empathy moderates (or strengthens) the effect of the intervention, do I look at the interaction between empathy and the intervention, or do I simply add empathy as a "control" or "nuisance" variable in my model?
Apologies if this is a very basic question but there seem to be multiple definitions of the above terms all over the internet, so I would appreciate some clarity. Thanks!

ANCOVA assumes that the slopes relating outcome to covariate (CV) values are the same for all groups. That is, for your IV (factor) of primary interest, there is no IV:CV interaction term related to outcome. That simplifies interpretation, as you can then assess associations of the IV with outcome independent of the value of CV.
In the broader context of linear models you don't need to worry about the ANCOVA terminology. Depending on your knowledge of the subject matter, you might try to "control for" a variable with a simple additive term or with an interaction between it and other predictors in your model. If you specify interaction terms involving the primary IV then the model might no longer be considered ANCOVA, but it's still an interpretable linear model. You then have to be careful to specify particular sets of predictor values for comparison, however, as there is no longer a single IV effect independent of CV values.
You should consider "moderator" and "interaction" to be equivalent. If your knowledge of the subject matter suggests the possibility of moderation, then include interactions between those predictors.
