Assume that we suddenly connect a battery to two wire ends. These may be separate wires or the ends of a single wire and the wire may be infinitely long or very short. The initial surge of current into this wire is completely determined by the spacing and the thickness of the near wire ends at the time of connection (initial surge is something that happens in the first few picoseconds).
If we had connected a current source instead of a battery to the two wires the initial voltage surge would also be totally determined by the wire geometry. By changing the spacing of the external wires we would find the initial voltage surge to be directly related to the wire spacing. The ratio of voltage V to the current I is strictly a geometric property of the wires and is called the characteristic impedance of the wire configuration.
From the initial surge one cannot tell whether the source is of a voltage or of a current type. The ratio V/I established initially persists along the whole length of the wires provided they are of uniform thickness and uniformly spaced along the whole length. But if the geometry changes at some point along the wire, the ratio V/I accommodates to whatever the wire spacing and diameter demand. In the process a correction is sent back to the source. At such time the distinction between a voltage and a current source becomes very apparent. A detailed study, at the electron level, will reveal the true nature of the processes responsible for the behaviour just described.