(the addition) a collection of Oral Torah supplementing the Mishnah. Compiled about 220-230 A.D., a generation after the Mishnah.
(Aram. "supplement"): a body of teachings authored during the same period as the *Mishnah, but not included in that text; when not capitalized, the term refers to a single teaching of this type
Tannaitic supplements to the Mishnah. Called hberaita/ (extraneous material) in the Talmud.
(Aramaic): "Addition." The term refers to material which was contemporaneous with the Mishnah but which Rabbi Judah the Prince did not include in that work. Organized in a manner very similar to the Mishnah, the Tosefta is attributed to Rabbi Hiyya and Rabbi Oshaya.
A collection of teachings by the same guys that wrote the Mishnah, but with a bit less authority in traditional Jewish jurisprudence.
The Tosefta is a secondary compilation of the Jewish oral law from the period of the Mishnah.