In the Gemara, the phrase תנו רבנן (Tanna Rabbanan) introduces various sorts of teachings. Are these teachings exclusively Tannaic or Amoraic in source?
These sources are generally Tannaic in nature. They usually introduce what my Gemara Rebbe in yeshiva referred to as "well-known beraitot".
The following is a quote from the Wikipedia article about beraitot
Here, a teaching from the Baraita is usually introduced by the Aramaic word "Tanya" ("It was orally taught") or by "Tanu Rabanan" ("Our Rabbis have orally taught"), whereas "Tnan" ("We have orally taught") introduces quotations from the Mishna.
As @DoubleAA rightly pointed out in the comments, like any "rule" there are exceptions. Tannu Rabanan is definitely used occasionally to quote mishnas and I believe it is even occasionally used to quote amoraic discussions.