1. זרוע לחיים וקבה only applies to chullin (חזה ושוק only applies to kodashim)

The tenth Perek begins: הזרוע והלחיים והקבה נוהגין בארץ ובחוצה לארץ – the obligation to give the foreleg, jaws and abomasum (fourth stomach) to a Kohen applies both in Eretz Yisroel and outside Eretz Yisroel, and during and after the Beis Hamikdash. However, it only applies to chullin animals, not to kodashim. One might have derived otherwise from a kal vachomer: chullin is exempt from giving חזה ושוק – the chest and thigh to a Kohen, yet is subject to זרוע לחיים וקבה; therefore, kodashim, which is subject to the law of חזה ושוק, certainly should be subject to זרוע לחיים וקבה. The passuk therefore says ואתן אותם לאהרן הכהן ולבניו לחק עולם – I have given “them” to Aharon and his sons as an everlasting right, implying אין לו אלא מה שאמור בענין – he only has that which is mentioned in the context [of kodashim], i.e., the חזה ושוק.

The Gemara then attempts to derive from kodashim that chullin should likewise be subject to חזה ושוק, but concludes that this is impossible: חזה ושוק requires תנופה – waving, which must be "לפני ה'" (i.e., in the עזרה), but chullin may not be brought into the עזרה.

1. One who damages מתנות כהונה is exempt from paying (ממון שאין לו תובעין)

Rav Chisda says: המזיק מתנות כהונה או שאכלן פטור מלשלם – one who damages the Kohanim’s gifts or eats them before a Kohen receives them is exempt from paying. This may be derived from "וזה יהיה משפט הכהנים" – and this shall be the due of the Kohanim, implying that the obligation to give the מתנות only applies while they are in existence. Alternatively, the reason is משום דהוה ליה ממון שאין לו תובעים – because it is money which has no claimant, i.e., no specific Kohen owns them to claim damages. After a Kohen receives them, however, they are his personal property, and one who damages them must compensate him. A Baraisa indicates that Rebbe Eliezer holds one who eats מתנות designated for the poor, e.g., מעשר עני, is liable to pay, and considers them money which has claimants. However, the Gemara explains that the Chochomim argue, and require payment only as a מדת חסידות (Rashi says one must pay to fulfill his obligation בידי שמים).

1. מתנות כהונה may not be given to a כהן עם הארץ

Rav Chisda’s ruling is challenged from a Baraisa which states: וזה יהיה משפט הכהנים – and this shall be the law of the Kohanim, מלמד שהמתנות דין – teaching that the מתנות are law to be enforced by דיינים. Presumably this means להוציאן בדיינין – to collect [the מתנות] with judges, with the first Kohen to claim able to compel the owner to give them to him. If so, מתנות כהונה do have claimants!?

The Gemara answers that the Baraisa means לחולקן בדיינין – to distribute them according to the judges’ direction. As Rebbe Yonasan said: מנין שאין נותנין מתנה לכהן עם הארץ – from where do we know that we do not give a מתנה to a Kohen who is an עם הארץ? The passuk says that the king instructed the people to give the "מנת" – portion to the Kohanim and Leviim, "למען יחזקו בתורת ה'" – so that they will hold firmly to Hashem’s Torah. This teaches: כל המחזיק בתורת ה' יש לו מנת – any Kohen who holds firmly to Hashem’s Torah has a right to a portion, ושאינו מחזיק בתורת ה' אין לו מנת – but any Kohen who does not hold firmly to Hashem’s Torah has no right to a portion.

Siman – Kol (Chazan). The chazan on his way to give זרוע לחיים וקיבה while singing about the fact that they are given only from חולין and not קדשים, who got so hungry that he ended up eating them but was exempt from paying because they are ממון שאין עליו תובעים, was on his way to give the matanos to a בית דין that was going to distribute them only to Kohanim who were not עמי הארץ.