The rod and staff were striking weapons, like clubs, (Until recently a prohibited weapon in Texas) to defend the flock and I believe the shepherd David may have used such in killing the lion and the bear.
[34] And David said unto Saul, Thy servant kept his father's sheep, and there came a lion, and a bear, and took a lamb out of the flock:
[35] And I went out after him, and smote him, and delivered it out of his mouth: and when he arose against me, I caught him by his beard, and smote him, and slew him.
[36] Thy servant slew both the lion and the bear: