From where do we derive these halakhot with regard to a sin offering brought for idol worship, which has unique halakhot, as detailed in Numbers 15:27–31, and with regard to which the term: For a sin offering, is not written? Likewise, from where do we derive them with regard to the sin offerings that are brought for the hearing of the voice, and for an utterance of the lips, and for the defiling of the Temple or its sacrificial foods, which also have unique halakhot (Leviticus 5:1–13), and with regard to which the term: For a sin offering, is not written either?
חטאת דעבודה זרה – אתיא מחטאת חלב, שכן כרת כמותה; והנך כולהי – אתיין במה הצד.
The Talmud answers: With regard to a sin offering brought for idol worship, these halakhot are derived from the halakhot of a sin offering brought for eating forbidden fat, as idol worship is also punishable by karet, similar to consumption of forbidden fat. And with regard to all these other sin offerings, which are brought for transgressions not punishable by karet, these halakhot are derived by analogy from the common element of the aforementioned 3 sources, namely, a standard sin offering, the sin offering of a nazirite, and the sin offering of a metzora.
תנו רבנן: פסח בזמנו – לשמו כשר, שלא לשמו פסול; ובשאר ימות השנה – לשמו פסול, שלא לשמו כשר.
§ A baraita states: When a Paschal offering is sacrificed at its appointed time, on Passover eve after noon, if it is sacrificed for its sake, it is fit; if it is sacrificed not for its sake, it is unfit, as stated in the Mishnah. And when an offering consecrated as a Paschal offering is sacrificed during the rest of the days of the year, if it is sacrificed for its sake, it is unfit; if it is sacrificed not for its sake, it is fit.