"Moderation" versus "interaction"? I have come across these two terms which are used interchangeably in many contexts.
Basically, a moderator (M) is a factor that impacts on the relationship between X and Y. Moderation analysis is usually done using a regression model. For example, gender (M) can affect the relationship between "product research" (X) and "product purchase" (Y).
In interaction, X1 and X2 interact to influence Y. The same example here is that "product research" (X1) is affected by "gender" (X2) and together they affect "product purchase" (Y).
I can see that in moderation, M affects the X-Y relationship but in interaction, M (which is gender in this case) affects the other IV. 
Question: If the aim of my project is to see how gender affects the relationship between X and Y, should I use moderation or interaction?
Note: My project is about the correlation between X and Y, not causal relationship between X and Y. 
 A: I think you have things mostly correct except for the part about "in interaction, M (which is gender in this case) affects other the IV."  In an interaction (a true synonym for a moderator effect--not something different), there is no need for one predictor to influence the other or even be correlated with the other.  All that is implied by "interaction" (or "moderator") is that the way one predictor relates to the outcome depends on the level of the other predictor.  
A: You should consider the two terms to be synonymous.  Although they are used in slightly different ways, and come from different traditions within statistics ('interaction' is associated more with ANOVA, and 'moderator variable' is more associated with regression), there is no real difference in the underlying meaning.  In fact, statistics is littered with synonymous terms that come from different traditions that mean the same thing.  Should we call our X variables 'predictor variables', 'explanatory variables', 'factors', 'covariates', etc.?  Does it matter?  (No, not really.)
The way to think about what an interaction is, is that if you were to explain your findings to someone you would use the word 'depends'.  I will make up a story using your variables (I have no way of knowing if this is accurate or even plausible):  Lets say someone asks you, "if people research a product, do they purchase it?"  You might respond, "Well, it depends.  For men, if they research a product, they typically end up buying one, but women enjoy looking at and thinking about products for its own sake; often, a woman will research a product, but have no intention of buying it.  So, the relationship between researching a product and buying that product depends on sex."  In this story, there is an interaction between product research and sex, or sex moderates the relationship between research and purchasing.  (Again, I don't know if this story is remotely correct, and I hope no one is offended by it.  I only use men and women because that's in the question.  I don't mean to push any stereotypes.)
A: Moderation Vs Interaction
Both moderation and interaction effects are very much similar to each other. Mathematically, they both can be modelled by using product term in the regression equation. Often researcher use the two terms as synonyms but there is a thin line between interaction and moderation. The difference between the two is broadly similar to the difference between correlation coefficient and regression coefficient.
When we say X and Z interact in their effects on an outcome variable Y, and there is no real distinction between the role of X and the role of Z.  They are both considered predictor variables. Then we identify this effect as interaction effect. 
While, in case we have clear distinction between the predictor and moderator variables (on the basis of theory) and we are interested to see the impact of predictor on response (affected by moderator), then this effect is known as moderation effect. One should carefully choose the term which is more suitable to answer one’s research question.
For detailed comparison of these terms, refer 
http://learnerworld.tumblr.com/post/147085936920/interaction-moderationenjoystatisticswithme
and 
http://learnerworld.tumblr.com/post/147089718705/mediationmoderationinteractionenjoystatisticswithme 
A: I think the most general model one can write regarding moderation of a variable z "in a relationship between y and x" is:
y = f(x) + g(z) + h(x)z
The marginal effect of x is f'(x)+h'(x)z, so the moderation effect is h'(x).
Mike
