1. There are a few parts to the Mishnah on 81a. The first two parts state that Chulin must be used, but the third part states that the Korban Todah must be brought from Ma'aser. The Machlokes Amora'im applies to the third part of the Mishnah.

2. The principle behind the Mishnah is that anything which one is obligated to bring must always be brought from Chulin (this is also stated explicitly in the Mishnah on 82a). Then, on 81b, Rav Huna says that if one states that he will bring "Lachmei Todah" -- the bread of the Todah offering -- he must bring the Korban Todah together with the bread. Even though he did not say explicitly that he would bring a Todah, he must have realized that one never brings the Lechem offering without the Todah, and thus when he said "Lachmei Todah" he really meant to say "Korban Todah together with the bread."

3. The Gemara questions Rav Huna from the third part of the Mishnah which states that if one said that he would bring a Korban Todah from Ma'aser and its bread from Chulin, then he brings exactly according to what he said. Why is this so, according to Rav Huna? Why do we not say that since he said he will bring the bread from Chulin, this means that he will also bring the Todah from Chulin? The Gemara answers that the third part of the Mishnah is different, because since he said explicitly that he will bring the Todah from Ma'aser, we must explain his additional statement -- that he will bring the Lechem from Chulin -- to mean that the bread comes merely to exempt the Todah offering, but the Todah itself is brought from Ma'aser, as he said explicitly.

4. In short, the discussion in the Gemara does not refer to a part of the Mishnah which says that he brings it from Chulin, but rather to a part of the Mishnah which says that he brings from Ma'aser.

G'mar Chasimah Tovah,

Dovid Bloom