Good catch, the dynamic friction equation should be =. Unfortunately we cannot replace the video on RU-vid. For the equations, Ff is used to describe the force of friction, as Fs and Fd are both described by this. It is important to understand that Fs and Fd are not two separate forces, but rather Ff in two different situations. As an object is pushed with increasing force, at any point in time the applied force = static friction (remember that ΣF = 0 at equilibrium so the forces must be equal). The maximum force of friction the object can exert is μsN. Once the applied force exceeds the maximum static friction, the object begins to move and the force of friction immediately decreases to μdN, ie dynamic friction. We hope you can appreciate how this is just friction in a static context and a dynamic context, hence why Ff is used.
