We investigate the differences between the light-cone distribution amplitudes (LCDAs) of B-s mesons and B-q mesons (with q = u, d) induced by a non-vanishing strange-quark mass m(s) & NOTEQUAL; 0 (compared to m(q) & SIME; 0). To this end, we consider the so-called "radiative tail" which is related to the short-distance expansion of the relevant light-ray operators in heavy-quark effective theory. We extend the calculation of the according matching coefficients, including operators linear in m(s) for both the leading and sub-leading 2-particle LCDAs. Based on a generic parameterization for the leading LCDA, we discuss the effect on its shape on a quantitative level, and compare our findings with recent results on the inverse moments of the B-q and B-s LCDAs from QCD sum rules.