Demai, Chapter 3, Mishnah 4. This mishnah presents us with the figure of the Kusi (Samaritan). The Kusim were a group of people whom the king of Ashur settled in Shomron at the end of the First Temple period, in place of the ten tribes. They converted out of fear of the lions that had begun to attack them, and the Gemara records a dispute as to whether they were genuine converts or not. Later in history, when they were found to be engaged in actual idol worship, the Sages declared them full non-Jews - even according to the opinion that they had originally been considered full converts - and all their laws are those of non-Jews.
Our mishnah deals with the period in which the Kusim were still accepted as Jews, except that they were generally suspect in matters of tumah and tithes; and the mishnah comes to teach the exception in this regard. There are several ways to explain the mishnah, and we will suffice with the explanation according to the commentary of the Rav (Bartenura).
Bringing wheat to a miller:
"HaMolich chittim l'tochen Kusi, o l'tochen am ha'aretz - b'chezkatan l'ma'aser v'lishvi'is" - One who brings his wheat to a Kusi miller or to a miller who is an am ha'aretz may assume that the flour he received back came from the wheat he gave, and that it was not switched with someone else's. Therefore, if he had already separated the tithe from it, it retains its status; and if these were produce of Shevi'is from before the time of biur (removal), which is still permitted to be eaten, unlike after biur, it too retains its status.
"L'tochen nochri - demai" - If the miller is a non-Jew, the flour he receives has the status of demai. Why? Because many people bring their wheat to that same miller, and there is reason to suspect that he switched his wheat with the wheat of another Jew who is an am ha'aretz - and therefore he must be concerned for demai.
Depositing produce for safekeeping:
"HaMafkid peirosav etzel haKusi o etzel am ha'aretz - b'chezkatan l'ma'aser v'lishvi'is" - Here too he may assume that they do not switch the produce with their own produce.
"Etzel nochri - k'peirosav" - One who deposits his produce with a non-Jew who is not a professional but a private individual with whom the produce was left for safekeeping, what he receives back has the status of the non-Jew's own produce, which is exempt from tithes. Therefore he may be lenient and say that even if he received produce belonging to the non-Jew, it is exempt from tithes.
What is the difference between the two cases? With a miller, who is a professional, one must be concerned for demai because many people bring their grain to him for grinding, and there is reason to suspect that he switched it with someone else's. But with a deposit, we are speaking of someone with whom this person left his produce personally, and there is no reason to assume that other Jews deposited produce with him as well; therefore, if he switched, he switched with his own.
"Rabbi Shimon omer: demai" - Rabbi Shimon disagrees and holds that even when depositing with a non-Jew the produce must be treated as demai, for just as this person deposited his produce with him, there is reason to suspect that other Jews deposited with him as well, and perhaps he switched the produce with theirs - and therefore what he receives back has the status of demai.
In summary: In this mishnah we learned the law regarding the Kusi, the am ha'aretz and the non-Jew in two cases: one who brings wheat to be ground - with a Kusi or an am ha'aretz the produce retains its status for tithes and Shevi'is, while with a non-Jewish miller it is demai, out of concern that it was switched with other people's grain; and one who deposits his produce - with a Kusi or an am ha'aretz it retains its status, while with a non-Jew it is treated "like his own produce" and is exempt from tithes, since if he switched, he switched with his own. Rabbi Shimon disagrees and requires treating it as demai here too, out of concern that other Jews deposited produce with him.