What can change in the rods?

As far as we know at this point, all three rods are identical from the user's point of view. The game may roll three different Magikarp, or it may simply roll one; given you know nothing to differentiate between the three those would be identical from a probabilistic point of view.

I've done a little research, but not statistics-level yet, to see if the choice seems to have any correlation to the type of bonus you get; in my research it doesn't seem to. I believe the three rods are a meaningless choice.