Looking at a couple of definitions it would appear that the purpose to which the item is to be put is relevent.
For instance a metal bar derives it name from the fact that it is used to prevent passage of something i.e. "To bar" as here:
1. a relatively long, evenly shaped piece of some solid substance, as metal or wood, used as a guard or obstruction or for some mechanical purpose: the bars of a cage.
2. an oblong piece of any solid material: a bar of soap; a candy bar.
3. the amount of material in a bar.
4. an ingot, lump, or wedge of gold or silver.
5. a long ridge of sand, gravel, or other material near or slightly above the surface of the water at or near the mouth of a river or harbor entrance, often constituting an obstruction to navigation.
6. anything that obstructs, hinders, or impedes; obstacle; barrier: a bar to important legislation.
This has now obviously evolved into relating to most cross sectioned lengths of material be it round, square, flat, hex etc..etc..
However this is one definition that I found for a "Rod":
Metallurgy. round metal stock for drawing and cutting into slender bars.
This would tend to indicate that bars must be flat and rod is round, square, hex etc.
And there again we order all our metal stock as "Bar Stock" whatever the cross section be it flat (Flat Bar) or round (Round Bar)
At the end of the day is there a right and a wrong?