Four hundred and thirty years after the patriarch Jacob had arrived with his household of seventy (and the Pharaoh of Egypt at the time of the Exodus then possibly Amenhotep II), the Israelites exit Egypt with panache, organized into 12 tribes.
Six hundred thousand men, aside from boys and women, will assemble at Mt. Sinai shortly thereafter.
The Israelites are organized into three ceremonial levels: These “classes” come into play in ceremonial matters relating to the Temple, in particular. The progenitor “Temple” was the “mishkan” of the desert. So the three “temple” classes were/are:
1) Priesthood (Ko–hen) holds prime Temple ceremonial duties; descendants of Aaron, brother of Moses; exclusively from the Tribe of Levi.
2) “Levite class”: Levites (Lai–vi) hold a variety of Temple ceremonial duties; from the Tribe of Levi.
3) Nation as a whole: Israelites (Yisrael) – from the other eleven tribes.
*
So, to clarify: From the Tribe of Levi, if one were a descendant of Aaron (brother of Moses), one was a Kohen; if one was from the Tribe of Levi, but not a descendant of Aaron, one was a Levite. All other Jews are the “Israelite class” in ceremonial matters. However, the term “Israelites,” unless specifically referring to Temple matters, 99.9 percent of the time refers to all 12 tribes.
*
After 40 years in the desert, the Israelites finally establish themselves in Canaan through a series of military victories and political ententes.