Gemara

(Beraisa): "Korbano (his Korban)" teaches that one is Yotzei with his own Korban, but not with his father's Korban;

Suggestion: One is not Yotzei for a severe sin with his father's Korban separated for a light sin, or vice-versa, but he is Yotzei for a sin of the same severity!

Rejection: "Korbano" - one is Yotzei with his own Korban, but not with his father's. (There are three occurrences of this word in the Parshiyos of Chatas.)

Suggestion: One is not Yotzei with his father's Korban, even for a sin of the same severity, just like a Nazir cannot use his father's Korbanos Nezirus;

However, he is Yotzei (if he buys an animal) with money that his father separated, even for a sin of a different severity, just like a Nazir is Yotzei with Stam money of his father, but not with specified money!

Rejection: "Korbano" - one is Yotzei with his own Korban, but not with his father's.

Suggestion: One is not Yotzei with money that his father separated, even for sins of the same severity, but he is Yotzei with an animal he separated for himself for a different sin, even if the other sin was of a different severity!

Rejection: "Korbano... Al Chataso" - his Korban must be for his sin (for which it was originally separated for).

Suggestion: If one separated a Korban for eating Chelev and offered it (b'Shogeg) for eating blood, or vice-versa, he did not transgress Me'ilah and did not get atonement. Therefore, even b'Mezid, if one offers an animal he separated for a different sin, even of the same severity, he was not Yotzei;

But if one separated money for a Korban for eating Chelev and (b'Shogeg) used it to buy a Korban for eating blood, or vice-versa, he transgresses Me'ilah and gets atonement. Perhaps he is Yotzei even b'Mezid with money he separated for himself, even for sins of different severity!

Rejection: "For his sin" - his Korban must be (from money) for his sin.

Kerisus 27b - Question: What does it mean "He was not Mo'el and it did not atone"?

Answer (Rav Shmuel bar Simi): Since he cannot be Mo'el, it did not atone;

Regarding money, if he changes the Kedushah, he is Mo'el and brings an Asham Me'ilah. One might have thought that he may do so l'Chatchilah! The Beraisa teaches that he may not.

(Mishnah): If one was Makdish a Chatas, he may not bring it for a different sin. Even if he was Makdish a Chatas for Chelev he ate yesterday, he may not bring it for Chelev he ate today. We learn from "Korbano... Al Chataso" - the Korban must be for the sin.

Zevachim 7a (Rava): If Reuven's Chatas was slaughtered l'Shem Chatas, it is Kosher (and he was Yotzei);

We learn from "V'Shochat Osah l'Chatas" - as long as it was slaughtered l'Shem Chatas, it is fully Kosher.

9b (Rava) Question: If a Chatas for eating Chelev was slaughtered to atone for entering the Mikdash b'Tum'ah or eating Kodshim b'Tum'ah, what is the law?

Since there is Kares for Tum'as Mikdash (just like for eating Chelev), it is Kosher?

Or, since a poor person can bring birds for Tum'as Mikdash (but not for Chelev), it is Pasul?

(Rav Acha brei d'Rava): Rava taught that in all cases (even if it was to atone for eating blood), it is Pasul. We learn from "V'Shochat Osah l'Chatas" - it must be slaughtered for the proper Chatas.

Rishonim

Rambam (Hilchos Pesulei ha'Mukdashim 15:6): If one slaughtered a Chatas for a different sin, e.g. he was Makdish it for eating Chelev and slaughtered it for eating blood, it is Pasul.

Rambam (Hilchos Me'ilah 4:5): If one separated a Chatas for Chelev and offered it for blood, he did not atone. Therefore, he did not transgresses Me'ilah. If one separated money for (Chatas) Chelev, and used it to buy a Korban for blood, if he was Shogeg he atoned, therefore he transgressed Me'ilah. If he was Mezid he did not atone, therefore he did not transgress Me'ilah.

Ri Korkus: Rav Shmuel explained that an unblemished Korban cannot become Chulin, therefore he cannot change its Kedushah. When one is Mo'el (transgresses Me'ilah) with money, it becomes Chulin. One might have thought that even l'Chatchilah he may do so. The Rambam distinguishes between Shogeg and Mezid, for b'Shogeg he was Mo'el and the money became Chulin, so it is as if he bought a Korban with Chulin money.

Question (Kesef Mishneh): The Gemara said that atonement depends on whether or not he was Mo'ei. The Rambam says the opposite!

Answer (Ri Korkus): Here the Rambam discusses Me'ilah, so he makes it the end. He already discussed Kaparah in Hilchos Pesulei ha'Mukdashim. Since he did not get Kaparah, he did not benefit, therefore he was not Mo'el.

Rambam (Hilchos Shegagos 3:3): One who separated a Chatas for Chelev may not offer it for Chilul Shabbos or eating blood, for it says "Al Chataso Asher Chota." If he did, it is Pasul. Further, they said that one who separated a Chatas for eating Chelev last night may not offer it for Chelev that he ate today. If he did so, it is Kosher.

Ri Korkus, cited in Kesef Mishneh: The Beraisa says that even if he changed from one sin to a similar one, i.e. both are lenient or severe, he did not atone. However, if he changed to atone for the same sin at a different time, e.g. he ate Chelev last night and today, this is "Al Chataso" and it atones. The Mishnah cited the verse for the first law (a different sin). The Rambam wrote 'further, they, i.e. Chachamim, said that a Chatas separated for eating Chelev last night may not be offered for Chelev that he ate today. This is only mid'Rabanan, so if he did so, he atoned. A Tosefta says that from one sin to another he did not atone. We infer that for the same sin, he would atone. Also, we learned that if a son brought his father's Korban, he did not atone. This is a Chidush only when it is for the same sin, for then had it been his Korban (for the same sin at a different time), he would be Yotzei.

Rebuttal (Lechem Mishneh): The Beraisa suggested that one could bring his father's Korban (for himself) for a different sin, and needed a verse to refute this! Some texts of the Rambam say that a Chatas for the same sin at a different time does not atone. The text that says that he did atone is primary.

Defense (Kiryat Sefer): Indeed, the Beraisa suggested that one could bring his father's Korban (for himself) the same sin, whether it was severe or light, and concluded that he cannot.

Question (Tosfos Nazir 2b DH she'Harei): Here, we say that a Chatas Chelev offered for eating blood does not atone. In Zevachim, it says that it is Kosher!

Answer #1 (Tosfos): When he was obligated to bring both of them, he uprooted the Chatas, and did not atone. When he was obligated to bring only for Chelev, his intent for blood does not uproot the Lishmah.

Answer #2 (Tosfos): Here, we say that he did not atone for eating blood. There is an opinion in Zevachim that he did atone for Chelev.