Explanation #1: This refers to Olos of the Tamid or Musaf, that there are similar Korbanos [Olah] that are Nedavah;

However, Chata'os of the Tzibur, e.g. Se'irei ha'Regalim, even though they have a fixed time, were not offered;

We infer this, because it taught Pesachim. It should have taught only "what has a fixed time", and Pesach would be included!

Rather, you are forced to say that our Mishnah teaches that according to R. Shimon, other than Pesachim, they offered on a Bamah Gedolah only Chovos that have similar Korbanos Nedavah;

It means as follows. [The only difference] is Pesachim, which is offered on a Bamah Gedolah, but not on a Ketanah at all. Other matters, which are offered on both, there is no difference between them, just on this (Ketanah) they offered only Nedavos, and on this (Gedolah) they offered only Chovos with a fixed time, like Rashi explained.

Observation: Likewise, [the Gemara] could have inferred this from the Beraisa above (117a-b), in which R. Shimon said "even the Tzibur offered only..."

Implied question: There, R. Shimon does not discuss the difference between a Bamah Gedolah and Bamah Ketanah, like it discusses here!

Answer: In any case, he mentioned Pesach superfluously, for it was included in Chovos without a fixed time.

Question #1: What is R. Shimon's source for this, that Chatas with a fixed time was not offered?

Above, we explained that R. Shimon learns from Pesach of Gilgal. He cannot learn from Pesach, for also Pesach does not have something like it offered for Nedavah!

Answer: If we would explain that Pesach is considered that something like it is offered for Nedavah, because it is Kodshim Kalim, like Shelamim, this would be fine. However, Rashi did not explain like this.

Question #2: How did [the Gemara] infer from this that it taught Pesachim? Perhaps it taught Pesachim because the reason is learned primarily from Pesach!

Also in Megilah (9b), it taught only Pesachim, and the Gemara asked "is Pesachim the only difference?! Rather, like Pesachim";

You are forced to say that it mentioned Pesachim more than other [Chovos with a fixed time] because they are all learned from Pesach.

Explanation #2: "Explain your Beraisa to discuss Olah", i.e. since we learn from Pesach, we should say that just like Pesach has a fixed time, and it applies to a Tzibur like to an individual at a time that Bamos are permitted;

"A Tzibur" refers to Pesach Rishon, and "an individual" refers to Pesach Sheni, like it says in Pesachim (67a) that an individual is detained [to Pesach Sheni], but a Tzibur is not detained.

"Also everything with a fixed time, and it applies to the Tzibur like to an individual at a time of Heter Bamos" refers to Olos, which apply to the Tzibur regarding Tamid and Musaf, and to individuals, i.e. Nedavah;

However, Chatas, we do not find that it applies to an individual at a time of Heter Bamos, for even on a Bamah Gedolah they did not offer an individual's obligations according to R. Shimon, just like according to R. Meir and Rabanan.

Explanation #2 (cont.): Our Sugya means as follows. "Explain your Beraisa to discuss Olah", for there is Olas Nedavah, and an individual's Nedavos are offered, and it is like Pesach;

Whereas Chatas, do we find an individual's Chatas? An individual's obligations were not offered, not Olos and not Chata'os!

[The Gemara] asks that we should establish it to discuss a Minchah, for there is Chavitim, and it answers that a Minchah is not offered on a Bamah.

Question: We should establish it to discuss Shelamim, e.g. Kivsei Atzeres, for there are Shelamim of Nedavah!

Answer (Rashi): Kivsei Atzeres are Kodshei Kodoshim, and Shalmei Yachid are Kodshim Kalim. We do not find a similar Korban of an individual.