When a test charge stands next to a wire, there are coulomb forces between the test charge and the protons of the wire. 1: When the test charge starts to move, the Coulomb forces stays the same, because distances from test charge to protons stay the same. There is no magnetism in this case. 2: When the test charge stays still and the wire starts to move, the Coulomb forces increase, because distances from test charge to protons decrease. But we do not call this magnetism. We call it decrease of distance and increase of Coulomb force. If we ask the test charge, it says there is no difference between the case 1 and the case 2. In both cases the wire looks the same to the test charge. 3: When two test charges placed side by side start to move there is no change of distance, but there is a change of total force between the charges. This case we call magnetism. And we explain the 'magnetism' by the change of the electric fields. Right? 4: And the same change of fields can explain the total force between two wires with opposite currents.