Retrieving fallen produce while washing your hands in a stream

Question

In Machshirin 4:7, we learn:

‮פֵּרוֹת שֶׁנָּפְלוּ לְתוֹךְ אַמַּת הַמַּיִם, פָּשַׁט מִי שֶׁהָיוּ יָדָיו טְמֵאוֹת וּנְטָלָן, יָדָיו טְהוֹרוֹת וְהַפֵּרוֹת טְהוֹרִים. וְאִם חָשַׁב שֶׁיּוּדְחוּ יָדָיו, יָדָיו טְהוֹרוֹת וְהַפֵּרוֹת בְּכִי יֻתַּן:

If produce fell into a channel of water, and one whose hands were unclean put out his hands and took it, his hands become clean and the produce [also] remains clean. But if his intention was that his hands should be rinsed, his hands become clean and the produce comes under the law of ‘if water be put.’

In his commentary, the Bartenura writes that the person's hands are clean only with respect to eating ḥullin; with respect to teruma and ḳodashim, the hand-washing requires intention to be effective.

Why is there such a distinction, and what is the source of this distinction?

Answer 1

(h/t to DoubleAA for linking this answer)

The mishna in Ḥagiga 2:6 says:

‮6 הַטּוֹבֵל לְחֻלִּין וְהֻחְזַק לְחֻלִּין, אָסוּר לְמַעֲשֵׂר. טָבַל לְמַעֲשֵׂר וְהֻחְזַק לְמַעֲשֵׂר, אָסוּר לִתְרוּמָה. טָבַל לִתְרוּמָה, וְהֻחְזַק לִתְרוּמָה, אָסוּר לְקֹדֶשׁ. טָבַל לְקֹדֶשׁ וְהֻחְזַק לְקֹדֶשׁ, אָסוּר לְחַטָּאת. טָבַל לְחָמוּר, מֻתָּר לְקַל. טָבַל וְלֹא הֻחְזַק, כְּאִלּוּ לֹא טָבָל:

If he immersed for unconsecrated [food], and was presumed to be fit to eat unconsecrated [food], he is prohibited from [eating second] tithe. If he immersed for [second] tithe, and was presumed to be fit to eat [second] tithe, he is prohibited from [eating] terumah. If he immersed for terumah, and was presumed to be fit to eat terumah, he is prohibited from [eating] holy things. If he immersed for holy things, and was presumed to be fit to eat holy things he is prohibited from [touching the waters of] purification. If one immersed for something possessing a stricter [degree of holiness], one is permitted [to have contact with] something possessing a lighter [degree of holiness]. If he immersed but without special intention, it is as though he had not immersed.

Rambam says in Hilchot She'ar Avot HaṬum'ot 13:2 that this is a Rabbinic enactment. He also says that washing without intention is effective for ḥullin (contrary to the simple read of the mishna), and Kesef Mishna comments that this is the conclusion of the gemara's discussion.