Bikkurim 2:2 vs. Maaser Sheini 5:10

Question

Bikkurim 2:2:

יֵשׁ בְּמַעֲשֵׂר וּבִכּוּרִים מַה שֶּׁאֵין כֵּן בַּתְּרוּמָה, שֶׁהַמַּעֲשֵׂר וְהַבִּכּוּרִים טְעוּנִים הֲבָאַת מָקוֹם, וּטְעוּנִים וִדּוּי, וַאֲסוּרִין לָאוֹנֵן. רַבִּי שִׁמְעוֹן מַתִּיר. וְחַיָּבִין בַּבִּעוּר. וְרַבִּי שִׁמְעוֹן פּוֹטֵר. וַאֲסוּרִין כָּל שֶׁהֵן מִלֶּאֱכֹל בִּירוּשָׁלַיִם. וְגִדּוּלֵיהֶן אֲסוּרִים מִלֶּאֱכֹל בִּירוּשָׁלַיִם אַף לְזָרִים וְלַבְּהֵמָה. רַבִּי שִׁמְעוֹן מַתִּיר. הֲרֵי אֵלּוּ בַּמַּעֲשֵׂר וּבַבִּכּוּרִים, מַה שֶּׁאֵין כֵּן בַּתְּרוּמָה:

‎Ma'aser and Bikkurim share [laws] that are lacking in Terumah: that Ma'aser and Bikkurim must be brought to a [specific] place, require verbal recitation, and are prohibited to an Onen [a person whose close relative has died but has not yet been buried], while Rabbi Shimon permits. They both require removal [from one's home], while Rabbi Shimon exempts. Any amount of them [when mixed with normal food] is prohibited to eaten in Jerusalem. Any growth that comes from them may not be eaten in Jerusalem, neither by a non-Kohen, nor an animal, while Rabbi Shimon permits. All of the above is for Ma’aser and Bikkurim, but not for Terumah.

The Bartenura on R’ Shimon’s lenient rulings on Onen and removal limits it to Bikkurim. By Ma’aser, everyone agrees that the verses in the section of Vidui Ma’aser apply, including לא אכלתי באני - “I did not eat it as an Onen” - and the preceding several verses regarding destroying said Ma’aser. However, Bikkurim is called Terumah, and therefore, just as Terumah is exempt from these laws, so, too, Bikkurim.

TLDR: According to everyone, Terumah is exempt from the laws of Onen and destruction, learned out from the verses in Vidui Ma’aser.

Now compare to Ma’aser Sheini 5:10:

בַּמִּנְחָה בְיוֹם טוֹב הָאַחֲרוֹן הָיוּ מִתְוַדִּין. כֵּיצַד הָיָה הַוִּדּוּי, בִּעַרְתִּי הַקֹּדֶשׁ מִן הַבַּיִת (דברים כו), זֶה מַעֲשֵׂר שֵׁנִי וְנֶטַע רְבָעִי. נְתַתִּיו לַלֵּוִי, זֶה מַעְשַׂר לֵוִי. וְגַם נְתַתִּיו, זוֹ תְּרוּמָה וּתְרוּמַת מַעֲשֵׂר. לַגֵּר לַיָּתוֹם וְלָאַלְמָנָה, זֶה מַעֲשַׂר עָנִי, הַלֶּקֶט וְהַשִּׁכְחָה וְהַפֵּאָה, אַף עַל פִּי שֶׁאֵינָן מְעַכְּבִין אֶת הַוִּדּוּי. מִן הַבַּיִת, זוֹ חַלָּה:

‎By the afternoon of the last festival day, they would make the declaration. How was the declaration made? "I have removed the Kodesh [consecrated material] from the house" (Deuteronomy 26:13)--this is Ma'aser Sheni and Neta Revai. "Have given them unto the Levite"--this is Ma'aser Levi [The first tithe of produce, which must be given to the Levi]. "And also I have given it"--this is Terumah and Terumat Ma'aser. "And also to the stranger, to the orphan, and to the widow"--this is the poor man's tithe, Leket [fallen gleanings given to the poor], Shikhecha [forgotten gleanings given to the poor], and Pe'ah [corner of a field given to the poor], even though these do not invalidate the confession [if they have not been given]. "From the house"--this is Challah [dough that must be set aside for the priest].

Emphasis is mine.

If Terumah is included in Vidui Ma’aser, it stands to reason that the laws of Onen and destruction, learned from said passage, should apply to Terumah as well, and if so, Bikkurim should also be included.

Are we forced to say that there is a machlokes Tannaim, and according to the Tanna in Ma’aser Sheini, Terumah is indeed included in those laws? If so, how do the Tannaim in Bikkurim learn the passuk expounded in Ma’aser Sheini to include Terumah?

---

^{All quotes come from Sefaria.}

Answer 1

My understanding is that the mention of teruma in the vidduy is to fully list the different things that had to be given. The mishna in Bikkurim says that ma'aser and bikkurim both require vidduy, whereas teruma doesn't require vidduy. The Bartenura comments on this mishna that although teruma is mentioned as part of the vidduy in the words וְגַם נְתַתִּיו, someone who gives only teruma and not ma'aser and bikkurim wouldn't say the vidduy. The legal difference is only that you can't say the vidduy if you didn't bring each of those things (though the mishna in Ma'aser Sheni itself notes that there are exceptions even to this), but not to include everything listed under the same laws.

This is similar to the way that when a sota is required to swear that she didn't have relations with this man, she also has to swear about any other man (Sota 2:5). This doesn't mean the laws are the same between the case of this man and any other man (because only this man could have triggered the sota process), but once she is obligated to make the statement, the Torah requires her to include any other man as part of it. I think that the same is true in this case: the Torah requires someone who says the vidduy to declare that he disposed of his teruma and other tithes correctly, without necessarily implying that the rules of all the cases mentioned are the same.