וְגַם אֶת־אַחֶיךָ מַטֵּה לֵוִי שֵׁבֶט אָבִיךָ הַקְרֵב אִתָּךְ וְיִלָּווּ עָלֶיךָ וִישָׁרְתוּךָ וְאַתָּה וּבָנֶיךָ אִתָּךְ לִפְנֵי אֹהֶל הָעֵדֻת׃
You [Aharon] shall also associate with yourself your kinsmen the tribe [matteh] of Levi, your ancestral [literally father's] tribe [shevet], to be attached to you and to minister to you, while you and your sons under your charge are before the Tent of the Pact. (Bamidbar 18:2)
- Some say that between "stick" and "tribe" the term meant "scepter." (The Hebrew word for scepter - sharvit שרביט - may have derived from shevet as well.) That symbol of leadership became associated with the leader of the tribe itself, and then to the tribe he led. This intermediate stage is found in Bereshit 49:10, for example. Based on how he presents the order of the definitions of shevet, I think this is Kaddari's approach. Since he presents that development for shevet, and not for matteh, perhaps he holds that matteh was influenced by shevet in that regard. (For more detail about how the meanings of the words developed, see this Hebrew article by Athalya Brenner. She finds the "missing link" of shevet referring to the actual leader, but that link is not found with matteh.)
- Stahl has a similar approach, and points out that the the shevet as a scepter signified the leader's power to beat and punish, which connects back to the etymology of the root.
- Ben Yehuda says that shevet (as stick) became "tribe" in the way a branch splits off from the main part of a tree. In the same way multiple tribes would be divisions of a single nation.
- Radak takes a different approach. He says that the "original" word was matteh. He writes that one leans (relies) on a matteh (as implied by the root of the word), and both shevet and matteh as "tribe" refer to something you can rely upon. Perhaps he means that in tribal group everyone helps one another.
- Gesenius combines some of the above approaches, saying that shevet came to be tribe from the authority of the scepter, and matteh represents the branching out (as Ben Yehuda wrote about shevet). I suppose he viewed the developments of shevet and matteh as parallel, but independent.
And while in Modern Hebrew matteh has a primarily military connotation, shevet has much more of a civilian tone, used either for groups in youth movements, or to represent an ethnic or large family group (sometimes in a derogatorily way, similar to the English "tribal.")
As I've said before, Hebrew just can't handle synonyms...