If two electron beams are travelling side-by-side, then, from the point of view of an observer relative to whom they are moving, the force between them has two components, one electrostatic and the other magnetic. But from the point of view of an observer who is travelling with them, the electrons in both beams are stationary so there is no current and the only force is electrostatic. The Lorentz transformation explains the difference in terms of a change of the distances between the charges in their direction of motion (and so a change of the charge densities in the beams); but regardless of that, what is seen as a sum of “electric” and “magnetic” forces in one frame is seen as just an “electric” field effect in the other, and so there is no inherent observer-independent distinction between the electric and magnetic components. The formulation in terms of a second order tensor allows us to express both the apparent electric and magnetic fields seen by an observer as aspects of a single Lorentz invariant tensor field; but while it describes how they are related as aspects of a single tensor field, I wouldn’t really say that it shows they are so related.