(a) The word "Matnita" in "b'Matnita Tana" actually refers to a Tosefta (the Tosefta is a collection of Beraisos which were taught after the redaction of the Mishnah as an explanation of the Mishnah by the Tana'im. In the case of the Tosefta quoted on this Daf, this statement does not appear in our version of the Tosefta (which is printed at the end of the standard volume of the Gemara).

(b) When the Gemara uses the term "Matnitin" (in contrast to "Matnita"), it refers to the Mishnah, the first general redaction of Torah sh'Ba'al Peh, the Oral Law, comprised of the Six Orders covering all of the Halachos of the Torah. It was redacted by Rabeinu Yehudah ha'Nasi, also known as Rabeinu ha'Kodesh, or "Rebbi" for short. (He collected all of the teachings from all of the other Tana'im which they had received from their teachers, and based on those teachings he complied the six orders of the Mishnah; see RASHI in Bava Metzia 34b, DH Bimei Rebbi.)

When the Mishnah or Beraisa is quoted in the Gemara, you can tell by the word that introduces it whether it is a Mishnah or a Beraisa. "Tenan" means "we have learned in the Mishnah." "Tanya" means "it was taught in a Tosefta (or Beraisa)," while "Tanu Rabanan" means "the Rabbis taught in a Beraisa."

For a more detailed description, we recommend the short essay by Rav Shmuel ha'Nagid (993-1060 C.E.), "Introduction to the Talmud," printed in English by Rabbi Aryeh Carmell in his booklet, "Aiding Talmud Study" (Feldheim Publishers). You can also read the original Hebrew version as it is printed in the standard volume of Gemara, after Masechet Berachot (page 86, the short part in the middle of the page).