Electromagnetic and kinematic boundary conditions for surface waves propagating on the plane interface between a vacuum and a drifting plasma or a stationary plasma are investigated using a specular reflection procedure. The boundary values of specular-reflection solutions are shown to agree with the kinematic relations involving surface charge and surface current. The specular-reflection solutions explicitly show the well-known fact that a cold fluid forms a surface charge on the interface while a warm fluid does not. If the plasma is drifting (beam), the cold fluid forms a surface current in addition, whereas a warm fluid forms neither a surface charge nor a surface current. Consequently, in a drifting cold plasma, the tangential magnetic field, as well as the normal component of the induction vector D is not continuous. We show that the specular-reflection procedure and the conventional matching method yield the same dispersion relations, as they should, and we correct the wrong notion found in literature that the two methods somehow yield different results.