Rod and Staff (Psalm 23)

The shebat (rod) has the meaning of a 'tribe' or a 'sceptre'. The primary role of the king was to protect his people. The rod is symbolic of the power of God in discipline for his own and judgement for others. It is a protection from danger from within and without. A closely related word 'Shabbath' means 'rest', which is possible under the competent protection of the shepherd.

The mishenah or staff has the meaning of support. The Mishnah is a collection of early oral tradition of the Torah and is a support. It is used to draw sheep to the shepherd.

David knew well the meaning and the use of the rod and the staff, and he did not use the terms redundantly. Unfortunately, many translations mix them up calling a staff a rod and a rod a staff.

Addressing the idea that they are one tool, this is unlikely. An animal associates discomfort and pleasure with the object that causes it. If you use a rod to discipline an animal, it will shy from it, making the tool useless for comforting it. It is important that the two tools are visibly different.

It is more likely that modern shepherds who use only a single tool are often hirelings, and do not build individual trust with the sheep. So they care only for utility, (lengthening the arm) rather than the trust with the animal.