Challah, Chapter 1, Mishnah 6. This mishnah presents what appears to be two separate disputes between Beis Shammai and Beis Hillel. The commentators explain, however, that in truth it is a single dispute: although the mishnah describes it in terms of two different items, both items share one and the same law, and the very same disagreement between Beis Shammai and Beis Hillel applies to both.
The difference before us stems from two tannaitic traditions regarding the positions of Beis Shammai and Beis Hillel: one tanna understood that Beis Shammai are the ones who obligate and Beis Hillel are the ones who exempt, while the second tanna held the reverse - and each of them said what he said with regard to both the me'isah and the chalitah.
The two types of cases:
"HaMe'isah" - taking flour and putting it into boiling water.
"HaChalitah" - taking boiling water and pouring it onto the flour.
In both cases the law is one and the same, and the only question is what that law is according to each of the two tannaim.
The wording of the mishnah: "HaMe'isah - Beis Shammai potrin uBeis Hillel mechayvin" - Beis Shammai say that it is exempt from challah, and Beis Hillel obligate it. And afterward: "HaChalitah - Beis Shammai mechayvin uBeis Hillel potrin" - here Beis Shammai are the ones who obligate, and Beis Hillel are the ones who exempt.
From reading the mishnah one might have thought that the me'isah and the chalitah have different statuses and different laws, but that is not the reality, and both share one law. Rather, the first opinion, which holds that Beis Shammai exempt and Beis Hillel obligate, says so regarding the me'isah and the chalitah alike; and the second opinion, which holds that Beis Shammai obligate and Beis Hillel exempt, likewise says so regarding both. All that changed is the manner of presentation: one position was presented through the me'isah, and the other through the chalitah - and the only distinction between them is the question of who exempts and who obligates.
The loaves of a thanksgiving offering and the wafers of a nazir:
From here the mishnah turns to discuss the loaves of the thanksgiving offering and the wafers of the nazir - the loaves brought together with the korban todah, and the types of meal offerings brought by a nazir. The distinction is as follows:
He made them for himself - exempt: One who makes them for the sake of his own personal offering is exempt from challah, since at the time of kneading the dough was consecrated and it remained consecrated, and consecrated dough is exempt from challah.
He made them to sell in the market - obligated: One who makes them in order to sell them to a nazir or to someone bringing a thanksgiving offering is obligated in challah.
And why is he obligated? Because we are dealing with a situation in which they may ultimately not be offered, and their owner is likely to eat them himself. At the time of preparation, even though they were made for the sake of an offering, the one making them knows that he may not find a buyer, and if he does not find one, he will eat them himself. Therefore there is no definite sanctity here, only potential sanctity, and since they will ultimately be eaten by him, they are obligated in challah.
In summary: In this mishnah we learned that the dispute between Beis Shammai and Beis Hillel regarding the me'isah and the chalitah is a single dispute, and the two tannaim differed only as to which of them obligates and which exempts. We also clarified the law of the loaves of a thanksgiving offering and the wafers of a nazir: one who makes them for himself is exempt, because the dough is consecrated at the time of kneading; and one who makes them to sell in the market is obligated, because their sanctity is not definite and they will ultimately be eaten by him.