The shepherd's rod is used to protect the sheep; the staff to correct them. The sheep finds comfort in both these instruments. The sheep needs both protection from his enemies and correction in the way.
The Lord Is My Shepherd: He Leads Me in Paths of Righteousness for His Name's Sake. -Psalm 23:3 He found me weary, and wounded, and wandering. When He passed by and saw me polluted in my own blood, He said unto me, "Live."