Voltage transmission
When people say that voltage is transmitted along transmission cables, they mean that the conductors in the cable cause the voltage at the far end to become the same as the voltage at the transmitting end.

For most amateur (and many professional) situations, we can regard this as instantaneous, and as a pure voltage 'magically arriving' at the far end, with no current flow.

In greater detail, what happens when we connect a voltage source to one end of a transmission cable is that an electromagnetic wave sets off into the cable. It consists of both a voltage wave, and a current wave, travelling at the speed of light (or nearly so). It's not until these waves get to the far end of the cable, and are reflected by a load or an open circuit, and these reflections travel up and down the cable several times, that eventually steady state conditions are reached and the current settles down to zero for an open cable, or it settles down to the right value for any given load.

For times that are long compared to the time it takes light to travel the length of the cable, we can disregard these waves.