Our Mishnah picks up exactly where the previous one left off: two vessels, one containing Terumah and one containing chullin, and we do not know which is which - so they are mixed up.
Setting up the case:
Let us label the two vessels A and B. One of them holds Terumah and one holds chullin, and we do not know which is which. Now the contents of vessel A fell into a third vessel, vessel C, which already contained chullin. Two possibilities have therefore arisen:
Vessel C now contains a mixture of chullin and Terumah.
Vessel C contains only chullin - the chullin that was in it to begin with, plus the chullin that was added to it.
The status of the vessels before the fall:
Vessel A and vessel B, each on its own, were a rabbinic doubt of Terumah. Since one of the two certainly contains Terumah, we cannot relate to them separately, and therefore we must be stringent with them in all the stringencies of Terumah - and at least according to Rabbi Meir, in the stringencies of chullin as well. The rule is to treat both of them as potential Terumah.
A doubtful medumah:
Once vessel A, which is a rabbinic doubt of Terumah, fell into vessel C which contained chullin, the mixture in vessel C is no longer classified as doubtful Terumah but rather as a 'doubtful medumah': either it contains none of the Terumah at all and is pure chullin, or it is a mixture of chullin and Terumah together. The law is that in such a case the mixture does not become medumah, meaning that the contents of vessel C are not considered a forbidden mixture, and it may be eaten like any chullin. The reason: the law of medumah is rabbinic, and in a case of rabbinic doubt we rule leniently. The Sages did not establish the law of medumah to apply to such a scenario, and wherever it is not certain that a medumah was created, they were lenient.
Vessel B and separating challah - the dispute between Rabbi Meir and Rabbi Yosei:
Vessel B, which did not fall anywhere, remains with its previous status - doubtful Terumah, in which one must be stringent with the stringencies of Terumah: only a kohen may eat it, it must be guarded in purity, and so on. Nevertheless, Rabbi Meir points out that its contents may be chullin; therefore, if one took the wheat in vessel B and made from it a dough of the required measure, even if he is a kohen - because of the possibility that this is chullin, he is obligated to separate challah from it. He may eat the challah himself, since he is a kohen, but the mitzvah of separating it he must fulfill.
"Rabbi Yosei poter" - as was explained in the previous Mishnah, Rabbi Yosei exempts this dough from challah. Even though the contents may be chullin and may be Terumah, he relates to it as a medumah mixture, and his position is that a medumah carries no obligation to separate challah.
When vessel B also fell into a separate vessel:
Just as the contents of vessel 1 fell into vessel 3, which was entirely chullin, and we said that it does not become medumah, so too if the contents of vessel 2 - which is equally in doubt, possibly Terumah and possibly chullin - fall into vessel 4, which is entirely chullin, the ruling is the same as the previous case: vessel 4 does not become medumah, since a doubtful medumah is not treated as medumah. All of this, however, applies when vessel 3 and vessel 4 are kept separate from one another.
When both of them fell into a single vessel:
If the contents of vessel 1 and vessel 2, one of which is certainly Terumah, fell into a single vessel - let us call it vessel 5 - which contained chullin, then vessel 5 now certainly contains Terumah, and its status is that of medumah: a forbidden mixture of chullin and Terumah together. However, the calculation is made according to the smaller of the two.
For example: vessel 5 contained one hundred units of chullin, and one unit fell in from vessel 1 and two units from vessel 2. It is indeed possible that vessel 2 was the Terumah, in which case there is not one hundred times as much chullin as Terumah. But we may be lenient and assume that the smaller of the two - vessel 1, from which one unit fell in - was the source of the Terumah; it turns out that there is one hundred times as much, and even more, against that one unit of Terumah, and in such a case we may be lenient and the mixture is permitted to be eaten.
By the same token, when the mixture did not contain one hundred times as much as the Terumah, so that he must sell it to a kohen, he sells it at the value of the total amount minus the smaller of the two.
An example of this: vessel 5 contained ten units of chullin, and one unit fell in from vessel 1 and two units from vessel 2; vessel 5 therefore holds thirteen units. Of these - if vessel 1 was the source of the Terumah, one unit is Terumah; and if vessel 2 was the source of the Terumah, two units are Terumah. Since the mixture has the status of medumah, it must be sold to a kohen, but it may be sold to him at the value of twelve units of chullin and one unit of Terumah, and not at the value of only eleven, because we attribute the Terumah to the smaller of the two.
The reason for the leniency:
As was explained in the previous Mishnah, the governing rule in monetary matters is that the burden of proof rests on the one who seeks to extract money from his fellow. The kohen who claims that he need not pay the full amount, since perhaps two of the thirteen units are Terumah, has no proof, and the burden of proof is upon him. As long as he has not proven that there are two units of Terumah here, we assume that only one unit is Terumah, and he must pay for the remaining twelve units.
In summary: In this Mishnah we learned the law of two vessels that were mixed up, one containing Terumah and one containing chullin, with no way of knowing which is which. When one of them fell into a vessel of chullin, a 'doubtful medumah' was created, and since the law of medumah is rabbinic, we are lenient and the mixture is not forbidden. Regarding the vessel that remained in its place we are stringent with the stringencies of Terumah, and Rabbi Meir and Rabbi Yose disagree as to whether one is obligated to separate challah from it. When both vessels fell into a single vessel, the mixture becomes a certain medumah, but we attribute the Terumah to the smaller of the two, both regarding nullification in one hundred times its volume and regarding the monetary calculation in the sale to the kohen, based on the rule that the one who seeks to extract from his fellow bears the burden of proof.