We consider the asymptotic interaction laws of pulses and fronts in the so-called semi-strong regime of strongly differing diffusion lengths for reaction-diffusion systems. An asymptotic expansion and matching approach is applied in a model independent unifying framework. In contrast to the universal laws of motion arising in weak interaction, semi-strong interaction comes in different types that we refer to as first and second order. For illustration, we focus on a class of examples that includes the Gray-Scott and Schnakenberg models.