The mishna says that the only two korbanos that MUST be from new grain and from E.Y. are the korban omer and shtei ha'lechem. The gemara says that the mishna is against the Tanna of the Braisa who allows that there is a mitzvah to bring the omer and shtei ha'lechem from new grain, but if they are brought from the old grain, they are kasher. There are a few conclusions that we can draw from this gemara. 1. All agree that ideally the omer and shtei halechem should be from the new grain. 2. The machlokes between the braisa and the mishna is whether the omer and shtei halechem brought from old grain would be a valid korban (braisa), or invalid (mishna). 3. There is no distinction between the omer and shtei ha'lechem, if one is valid from old grain then the other is also valid.
These seemingly obvious conclusions make the Rambam very difficult to understand. The Rambam writes about this din in 3 places. In Hilchos Issurei Mizbei'ach (6:15) he copies the language of the mishna implying that both omer and shtei halechem MUST be from new grain of E.Y. However, in Hilchos Temidin U'musafin, in the context of shtei ha'lechem (8:2) the Rambam writes - שתי הלחם אינן באין אלא מן הארץ ומן החדש שנאמר ממושבותיכם תביאו לחם תנופה, לא מצאו חדש יביאו מן העליה. The Rambam holds that shtei ha'lechem would be valid when brought from old grain. Yet, one perek earlier in the context of korban omer, the Rambam writes (7:8) that the omer must be brought from Eretz Yisroel but makes no mention of the requirement of being from the new grain. Furthermore, the Ra'avad makes a strange comment on the Rambam who permits the shtei halechem to be brought from old grain when no new grain is available - הלכה זו בהפך. It is very unclear what is bothering the Ra'avad. Perhaps the Ra'avad understands that it is more likely to permit grain from outside E.Y. since we hold that there is an issur chadash even in chutz la'aretz, rather than permit using old grain.
The Kesef Mishna struggles with the Rambam and suggests (2nd approach) that the Mishna holds that both omer and shtei halechem lichatchila must be brought from new grain, but bidieved can be brought from old grain. The tanna of the braisa holds that there is a distinction between omer and shtei ha'lechem - shtei ha'lechem even lichatchila can be brought form old grain and is only a mitzvah min ha'muvchar to be brought from new grain, whereas omer lichatchila must be brought from new grain. This approach understands that there is a difference between the terms "mitzvah" and "lichatchila". The term mitzvah implies that it is ideal but not necessary, whereas the term lichatchila implies that it is necessary but not essential to the kashrus of the korban. Therefore the Rambam would hold that we pasken like the braisa that the omer lichatchila must be brought from new grain, whereas shtei halaechem it is only ideal but can be brought from old grain. According to this approach, the tanna of the mishna can hold that both the omer and shtei ha'lechem lichatchila must be brought from new grain, and only bidieved can be brought from old grain - the Rambam paskens like the mishna. This is also the approach of the Maha'ri Kurkos, there are 3 levels: mitzvah min hamuvchar, lichatchila and bidieved. The only arguement between the braisa and the mishna is whether the din of bringing from new grain is lichatchila or just ideal, but all agree that if no new grain is available, it can be brought from old grain.
In the question and answer of the gemara, the gemara asks on the braisa how we permit the omer and shtei halechem from old grain - what do we do with the pasuk of ראשית, to which the gemara answers that is only l'mitzvah. The gemara then asks what about the pasuk by shtei halechem which says מנחה חדשה implying new grain, and answers that it is coming for something else. When the gemara initally asks from the pasuk of ראשית it isn't clear if the gemara is asking from the pasuk by the omer - ראשית קצירכם, or from the pasuk by shtei ha'lechem - קרבן ראשית תקריב. According to the approach of the kesef mishna, the gemara which asks from ראשית and answers that it is only l'mitzvah has to be speaking about the shtei halechem which lichatchila can be brought form old grain, but omer is not just l'mitzvah, it must lichatchila be brought from new grain. Similarly, Tosafos (bottom of page) seems to understand that the question is from shtei halechem because Tosafos understands that חדשה is emphasizing what we learn from ראשית and the repeat should be me'akeiv. However, according to the kesef mishna the repeat should only tell you lichatchila (since the first time is l'mitzvah), which is not like tosafos who understands that the repeat is to tell you it is me'akeiv. Rashi in the k'sav yad explains that the question from ראשית is both by shtei halechem and omer, to which the gemara is answering that it is only l'mitzvah - against the approach of the kesef mishna.
Tosafos d.h. masninisin, is quoted by the ma'ahri kurkos on the Rambam as holding that the mishna permits both the omer and shtei ha'lechem to be brought bidieved from old grain, implying that the braisa holds that even lichatchila it can be brought from old grain, just not l'mitzvah (which is like his approach and the kesef mishna approach in the Rambam). However, he seems to have a completely different girsa in Tosafos. According to our girsa, Tosafos seems to be saying the opposite. Tosafos says that the language of the mishna אינן באין אלא מן החדש is does NOT imply just lichatchila, which is against the braisa that holds it is only lichtachila. Tosafos seems to hold like rashi (k'sav yad) that there are only 2 categories: 1. l'mitzvah = lichatchila, 2. bidieved.