The material itself
The third comparison is the one that cannot be explained by shape at all — and it needs a new property to explain it.
Observation
Even when two wires made of different metals are given the same length and the same cross-sectional area, and the same potential difference is applied to both, the currents flowing through them are not equal.
Why they differ
The reason is that the two metals differ in a property of their own, quite apart from the size and shape of the piece. That property is called resistivity, and because the two metals have different resistivities, their resistances differ.
Resistivity
Resistivity is the property of a material that decides how much resistance a piece of it will have, for a given length and cross-sectional area.
Why nichrome keeps appearing
This is the reason the activities in this chapter keep reaching for nichrome rather than copper. Nichrome has a high resistivity, so a short piece of it already has a useful resistance; copper has a low one, which is exactly why copper is what connecting wires are made of.
Two of the three factors are yours; one belongs to the substance
You can cut a wire shorter or choose a thicker one. You cannot change what copper is. Resistivity is the part of a conductor's resistance that comes with the material and not with the piece.