Bikkurim, Chapter 2, Mishnah 2. Like the previous mishnah, our mishnah lists a set of laws shared by ma'aser sheni and bikkurim which do not apply to Terumah: "Yesh b'ma'aser u'vebikkurim mah she'ein kein biterumah" - there are features of ma'aser sheni and bikkurim that are not found in Terumah.
The points shared by ma'aser sheni and bikkurim:
"Shehama'aser vehabikkurim te'unim hava'as makom" - both must be brought to a particular place: ma'aser sheni is brought to Jerusalem and eaten there, and bikkurim are brought to the Beis HaMikdash. Terumah, by contrast, does not need to be brought anywhere; as long as it is given to a kohen, it may be anywhere.
"Ute'unim viduy" - the confession of the tithes is made twice in the shemittah cycle: after the third year and after the sixth year, at the time of Pesach. Someone who has not yet taken care of the ma'aser sheni in his possession or brought up his bikkurim addresses this in the confession and removes them. Although Terumah is also mentioned in the confession, one does not recite the confession of the tithes for Terumah alone. In this sense ma'aser and bikkurim are the essence of the mitzvah of the confession of the tithes, which is not the case with Terumah.
"Ve'asur le'onen" - an onen, someone who has just lost a close relative, may not eat ma'aser sheni and likewise may not eat bikkurim, whereas Terumah is permitted to him.
"Vechayavim beviur" - one is obligated to dispose of them at the time of the confession of the tithes, unlike Terumah, which need not be destroyed but is simply given to a kohen.
Rabbi Shimon's position on these two laws:
"VeRabbi Shimon matir" - regarding an onen. What is he permitting? It appears that he permits only bikkurim, since with ma'aser sheni the Torah states explicitly that it may not be eaten by an onen; with bikkurim, however, this is not stated explicitly, and in his view they are permitted to an onen like Terumah and not like ma'aser sheni.
"VeRabbi Shimon poter" - regarding biur. Here too he is referring to bikkurim and not to ma'aser sheni: bikkurim do not require removal, and they may be given to a kohen exactly like Terumah and not like ma'aser sheni.
Something that has a way of becoming permitted:
Continuing with the features shared by ma'aser sheni and bikkurim as against Terumah, the mishnah says that even if a tiny amount of ma'aser sheni or bikkurim became mixed into other produce, all of that produce takes on the status of ma'aser sheni or bikkurim, and it is not nullified. The reason: both are considered "a thing that has a way of becoming permitted" - there is a way for them to be eaten permissibly, since ma'aser sheni is eaten in Jerusalem, and bikkurim are eaten by a kohen in Jerusalem. Since there is a permitted way to eat them, they are not nullified. Terumah, by contrast, has no permitted way of being eaten by a non-kohen, and therefore it is nullified in one part out of a hundred.
It is worth being precise in the language of the mishnah: this law, that it is a thing that has a way of becoming permitted and is not nullified, applies in Jerusalem alone. Outside of Jerusalem there is no way to permit eating ma'aser sheni and bikkurim, and therefore they are nullified there.
Growths:
From the same principle the mishnah continues: if one plants items that come from ma'aser sheni or from bikkurim, even what grows from them may not be eaten in Jerusalem - meaning it may not be eaten in a manner that does not observe the sanctity of bikkurim or the sanctity of ma'aser sheni, or eaten in a state of tumah and the like, since the growths too are not nullified.
The mishnah further mentions that this is not nullified even with regard to a non-kohen or an animal, who cannot eat bikkurim. One might have argued that with respect to them it is not "a thing that has a way of becoming permitted," since for them there is no permitted way to eat it at all; but since there is a way for a kohen in Jerusalem to eat it permissibly, that status is retained even with regard to a non-kohen and an animal.
"VeRabbi Shimon matir" - specifically in the case of growths. In his view, once the item has been planted, it is nullified. In a mixture Rabbi Shimon agrees that it is not nullified, but with growths he holds that it is permitted.
In summary: "Harei elu bama'aser uvabikkurim mah she'ein kein biterumah" - all the items listed are shared by ma'aser sheni and bikkurim and do not apply to Terumah: being brought to a particular place, the confession, the prohibition to an onen and the obligation of biur, as well as the law of "a thing that has a way of becoming permitted," which is not nullified in a mixture or in growths in Jerusalem. Rabbi Shimon, by contrast, permits an onen, exempts from biur and permits growths, because he equates bikkurim with Terumah rather than with ma'aser sheni.