I can't fully answer your question, because I don't fully understand it. But let me try to say some helpful things.
It is important to understand that the word "linear" in the phrase "linear model" means that the model is linear in the coefficients. It has nothing to do with the powers of the explanatory variables. So, for example,
y(x) = alpha + beta1*x + beta2*x^2
is a linear model (assuming y is the response variable, and x is the explanatory variable).
y(x) = alpha * sin(beta * x)
is not, because of the non-linear dependence on the coefficient beta.
A linear model can have interaction terms:
y(x1,x2) = A + B*x1 + C*x2 + D*x1*x2
is a linear model with interactions.
When describing models that have interactions, you will sometimes refer to the linear terms. In the above, B*x1 and C*x2 are the linear terms, and D*x1*x2 is the interaction term. (The terminology can definitely be confusing.)
Regarding different calls to LinearModel.stepwise giving different results ... I think it would be best if you gave a couple distilled examples. Otherwise, we're just guessing at exactly what you mean.
