I posited this model: AIUI before Rebbe there was a "Sea of Tannaitic statements" Rebbe (OK his predecessors ;-) redacted these statements into a coherent whole. Rebbe organized them by seder, maseches, and chapter. One of his biggest tasks was to decide what NOT to include.
After Rebbe finished, Rabbi Chiyya and Rabbi (H)Oshiya said: "wait a minute! A LOT has been left out!" And so they gathered alternate or supplementary collections of their own. And thus we have different anthologies of Tannaitic material