The Mishnah is the basic compilation of the Oral law of Judaism; it was written compile around 200 CE. The Tosefta is a second compilation of oral law from that period. It is a Halakhic work which corresponds in structure almost exactly to the Mishna, with the same divisions for sedarim (orders) and masekhot (tractates). It is mainly written in Mishnaic Hebrew, with some Aramaic.
The Mishnah was redacted by Judah haNasi in consultation with members of the Academy, while the Tosefta was edited by Rabbis Hiyya and Oshaiah on their own, thus the Tosefta is less authoritative (Rashi in his commentary on Talmud Sanhedrin 33a).
In many ways the Tosefta acts as a supplement to the Mishna (tosefta means 'supplement'). The text of most of Tosefta agrees nearly verbatim with the Mishna, and often varies only slightly. The Tosefta offers authors' names for laws that are anonymous in the Mishna; It also augments the Mishna with additional glosses and discussions. The Tosefta as we have it today functions like a commentary on unquoted Mishnaic material; It offers additional haggadic and midrashic material, and it sometimes contradicts the Mishna in deciding Halakha (Jewish law), or in declaring in whose name a law was given.
Much of the tosefta is currently regarded as being written shortly after the Mishna was redacted. However, recent scholarship, especially by Professor Judith Hauptman reveals that the Tosefta draws on source material earlier than the later material in the Mishnah. It may well be that parts of the Tosefta predate the Mishnah.
Related: Oral law, Mishnah, Talmud, Gemara, Rabbinic literature, Halakha
External link: Full text at Mechon-Mamre