My textbook for my electromagnetic waves class mentions both propagation velocity and phase velocity separately, without specifically defining either. When I googled both terms, I couldn't find a significant difference in their written definition, but when looking for equations for phase velocity and propagation velocity, I am not able to find equations for propagation velocity for a lossy medium. My textbook gives equations for phase velocity for lossless, low-loss and lossy medium, but only gives the equation for propagation velocity in a lossless medium. For a lossless medium, they are both the equivalent, but I have no way of verifying this for a lossy case. Are they in fact the same, or do they differ mathematically in a lossy medium? Also, my textbook only describes them as "phase velocity" and "propagation velocity", so I am unsure if there are any other terms used to describe them.