Mishneh Torah — Transmission of the Oral Law מסירת תורה שבעל פה, Chapter 18

רָב חִבַּר סִפְרָא וְסִפְרֵי לְבָאַר וּלְהוֹדִיעַ עִיקְרֵי הַמִּשְׁנָה, וְרִבִּי חִיָּא חִבַּר הַתּוֹסֶפְתָּא לְבָאַר עִנְיְנֵי הַמִּשְׁנָה. וְכֵן רִבִּי הוֹשַׁעְיָה וּבַר קַפָּרָא חִבְּרוּ בַּרַּיְתּוֹת לְבָאַר דִּבְרֵי הַמִּשְׁנָה, וְרִבִּי יוֹחָנָן חִבַּר הַתַּלְמוּד הַיְּרוּשְׁלְמִי בְּאֶרֶץ יִשְׂרָאֵל אַחַר חָרְבַּן הַבַּיִת בְּקֵרוּב מִשְּׁלוֹשׁ מֵאוֹת שָׁנָה.

Rav composed the Sifra and the Sifre to explain the sources for the Mishnah. Rabbi Chiyya composed the ToseftaHe followed his master's [Rabbi Yehudah HaNasi's] footsteps [in composing a text for the public] to explain the matters he saw to be confusing in his master's work.This was called the Tosefta. Its intent was to explain the Mishnah and expound upon concepts that would require much effort to be derived from the Mishnah… to show how these ideas could be developed and deduced from the Mishnah. to explain the subjects [discussed in] the Mishnah. Rabbi Hoshaia and bar Kafra composed baraitot to explain the matters [discussed in] the Mishnah. Rabbi Yochanan composed the Jerusalem Talmud in Eretz Yisrael approximately three hundred years after the destruction of the Temple.