How to model whether differences in two variables vary across the levels of a third variable? Say we have a variable A (some interaction network metric, continuous, N=20), and we want to see if A varies across B (categorical variable, 2 levels) depending on the levels of a third categorical variable C (3 levels).
So I am interested in exploring whether the differences in my interaction 
network metrics (A) vary across environmental gradients (B), depending on the way I measure it (C) (i.e. Do I get different results regarding differences to environmental gradient depending on the way y measure it?).
An interaction model tells me the differences between every condition (every level combination) but I just want to know the differences of A against B conditional to the three C levels.
Another option is to calculate the differences between A and B, and use it as the dependent variable to build a model.
Is there another way to model this relationship with the raw data so that I do not have to calculate a new variable?
 A: If your main interest is in the difference, why do you not want to analyze it directly? You should tell us that! 
Meanwhile, you should start by making some plots (and show us). Since $C$ is categorical, in practice this could depend on the number of levels of $C$ (one reason we need some context and not only a very abstract problem description.) For the time being assuming not to many levels, some possibilities:


*

*scatterplot of $B$ versus $A$ colored according to $C$

*Tukey mean-difference plot (also known as Bland-Altman plot) also with colored points.  For an example see Agreement between methods with multiple observations per individual

*in place of colored points, you could make the plots as conditioning plots (for an example see Investigate correlation conditional on a threshold.) 
In case your two measurements $A,B$ is pre- and post some intervention or similar, see Best practice when analysing pre-post treatment-control designs
If you give some relevant context I will try to extend.
