As Mike said, purpose matters.
You are not lubricating the arbor on a revolver to ease friction between the arbor and the cylinder. Any oil would do for this, and in fact probably no oil is needed at all.
The purpose of a grease in this case is not for friction. It is to act as a physical barrier to prevent blow-by gasses and fouling from traveling down the arbor and causing the cylinder to bind up. Some revolvers (Rogers and Spencer, Ruger Old Army) helped solve this problem by adding a boss to the front of the cylinder to help redirect the blow-by gasses.
Grease works better than oil in this case because being viscous it is less apt to get blasted away as oil would.
None of this really matters if you are only shooting a cylinder or two and calling it quits before cleaning the gun. But if you are looking to do an afternoon's worth of shooting a greased arbor will keep things running smoothly.