In Parashat Mattot the word matteh is used in place of the more commonly found shevet? Why is that? They both mean tribes no?
Both words mean stick or rod, as in Ishaya 28:27 כי במטה יחבט קצח וכמון בשבט. The one strikes harder than the other according to flexibility. The word שבט designates a tribe, whilst the word מטה is the pole that identifies the שבט because each tribe has its identifying flag, sign and/or name engraved on it. Consequently, in Parashat Mattot, the tribes are called מטות because that is the way they camped in the desert, each tribe around its identifying pole.
Rav Hirsch writes on Bamidbar (30:2) at the beginning of the Mattos,
The Torah enables individuals, communities, and the entire nation to establish for themselves permanent norms for ensuring the faithful observance of the mitzvos. For this reason this section is addressed particularly to the nesi'im who significantly are here called Roshei Matos. As already noted in our commentary on chapter 1, "matteh" conceives of the tribe as a branch of the larger whole, with each branch working through its own unique characteristics to carry out the mission shared in common by the entire nation. It was the task of the roshei hamattos to attend to the customs arising from the individuality of each branch, and to attend also to common activities, aspirations, and purposes. It was their responsibility to properly channel all of these to promote the fulfillment of the national mission in accordance with the unique characteristics of each branch. The means for such activity, the prerequisite for the development of the nation as a whole and for communal life is the binding force of vows and of regulations instituted by man which is was the laws that now follow deal with. In addition, roshei hamattos are entrusted with hataras nedarim. They function as family counselors and spiritual advisors coming from among the people themselves. It is for this reason too that the section on vows in addressed first to roshei hamattos.
On the other hand, Rav Hirsch (Bamidbar 18:2) writes,
מטה is the horizontal direction which looks on the tribe as a branch of the basic stem, accordingly being on a line with the other tribes, so being excluded from the actual priestly service and would only be allowed to be allocated to assist at subsidiary offices. שבט is the tribe as an independent stem, 'stave', hence the word itself is an expression of strength and power, as a rule is the designation of the tribes of Israel in their independent strength and value - שבטי ישראל not מטות ישראל. So that שבט אביך is the tribe in which your father lives on in his specialty, your father who subscribes such an important quota to the Jewish national body, the tribe that by its unreserved devotion to the cause of God showed itself as the born guard of the Sanctuary. As שבט אביך, the Levites received their position and mission towards the people, which was represented by the guard of their camp round the Sanctuary in the wilderness, which belongs to the משמרת אהל מועד.
In these succinct words from Rav Yaakov Beasely:
The term "shevet" connotes power and authority. However, the word "matteh," staff, is essentially a support (from the Hebrew root n-t-h). In the context of a describing a group, it connotes mutual aid and sustenance.