It’s not really a contradiction. The repetition can be similar elements, rather than the same. One that comes immediately to mind is Proverbs 6:16, which says “There are six things the Lord hates/seven that are detestable to him:” It then goes on to list seven things. But six and seven are different.
I do think it’s likely that the rod and staff could have actually been the same item performing different functions. As pointed out, there’s not really any reason the shepherd crook can’t also be used for discipline. In fact, the word for staff, מַטֶּה ormatteh can also refer to a rod, according to the aforementioned Strong’s..
But, even if they are strictly separate items, and shepherds always carried both, the parallelism is still there, because both are similar items that can perform the other’s function.