Implied Question: The Gemara in Megilah (7b) deduces regarding this rule that there is no difference (between Shabbos and Yom Tov etc.) that regarding doing Melachos with the items used to prepare food the same law applies to both Shabbos and Yom Tov (that it is forbidden).

Implied Question (cont.): The Gemara there says that this Mishnah (there is no difference etc.) is unlike Rebbi Yehudah. Rebbi Eliezer is even more lenient than Rebbi Yehudah, as is stated later (137b). (How can our Gemara imply that this Mishnah is according to Rebbi Eliezer?)

Answer #1: It is possible to say that the Tana of this Mishnah holds like Rebbi Eliezer that we make a decree regarding Yom Tov because of Shabbos, but argues regarding Melachah with items used to prepare food.

Answer #2: It is also possible to answer that the Mishnah that there is no difference etc. in Megilah is regarding Torah laws. Our there is no difference etc. is the Mishnah in Beitzah (37b) regarding Rabbinic laws, and they are therefore not discussing the same thing.

Proof: This is clearly correct as the Gemara in Beitzah (ibid.) asks the same question as our Gemara, but it does not ask this question in Megilah (ibid.). The deduction in Megilah (ibid.) that Shabbos and Yom Tov are the same regarding items used to prepare food is not stated in Beitzah (ibid.).

Explanation: He holds that a vessel is not carried unless it is for the normal purpose for which it is usually carried during the week, as explained earlier (37a). Burning pieces of vessels is not normally done, and there it is not the reason it is normally carried during the week.

Explanation: This is referring to pieces of vessels that broke before Shabbos. If they broke on Shabbos, the Gemara says later (142b) that Rava holds of Muktzah and certainly of Nolad (and Rava would say it is Muktzah).