In an article for Vayikra 5774, Rabbi Cherki discusses two ways of looking at sacrifices - through the "Torah of Moses" and the "Torah of Aaaron"
The sequence of the sacrifices in the Torah portion of Vayikra is: Olah, Mincha, Shelamim, Chatat, Asham. However, the sequence in next week's portion, Tzav, is: Olah, Mincha, Chatat, Asham, Shelamim. That is, in Tzav the Shelamim – the Peace Offering - is moved from the middle of the list to the end. Clearly, the earlier a sacrifice appears in the list the more important it is from the point of view of the will of the Holy One, Blessed be He. The Olah, where the entire sacrifice is offered up to G-d, and the Mincha, consisting of grains that are offered as a sacrifice or eaten by the Kohanim, indicate a complete desire by a person to approach G-d, without the addition of any personal interests, such as eating the substance of the sacrifice. This is an ideological act with corresponds to the basic trait of a sacrifice as an offer by the person out of pure love: "When a person offers from within you a sacrifice to G-d" [Leviticus 1:2]. The person's innermost desire is to offer himself up as a sacrifice. But just as at the Binding of Isaac G-d commanded, "Do not stretch out your hand" [Genesis 22:12], because G-d wants life and not death, so here too for all of the descendants of Isaac we are taught that all G-d wants is the intent of a person to be sacrificed, but not the actual sacrifice of his animal side, the physical body, which can be replaced by "a ram" [22:13], taken from cattle or sheep, and brought as a sacrifice.
The Shelamim is a more complex sacrifice, where the person participates in the "meal" at the Divine table. The Altar "eats," and so does the person who brought the sacrifice. But for this situation to be worthy, it is necessary for the eating by a man to be at a moral level worthy of the Altar. This type of service is limited to the level of the Children of Israel, who are capable of Divine intentions with respect to their eating. It is not relevant for the other nations, who can only bring an Olah sacrifice, since they have not yet reached the stage where they are able to incorporate their own bodily pleasure into the service of G-d.
The Chatat and the Asham are sacrifices meant to atone for sins. They are brought as a result of failure by a person and the need for mending the situation. These sacrifices are needed after the fact, and they therefore come at the end of the list.
However, the sequence discussed above is relevant in a case of when a person wants to give a contribution, based on ideals. Quoting from Rashi, "This refers to sacrifices that are given as a donation" [Leviticus 1:2]. This is closely related to the subject of the Torah portion of Vayikra, which is the beginning of a series of passages of the "Torah of Moses." These passages, which begin with, "And He called out to Moses" [1:1], describe the labor of a perfect man who is ruled by the intellect and who is far removed from any possibility of sin. The Torah portion of Tzav, on the other hand, is a direct continuation of the portion of Tetzaveh. (This is based on an analysis by Rabbi D.Tz. Hoffman, who concludes that Tetzaveh and Tzav were given as a single continuous passage, where the part that is linked to the appearance of the Shechina was written down in Exodus – in Tetzaveh – while what is relevant for later generations was written down in Leviticus.) The portion of Tzav emphasizes the obligatory aspect of the sacrifices as opposed to the tendency of mankind to try to avoid them. As Rashi notes, the goal is to "be wary in a case which entails monetary loss" [Leviticus 6:1]. Thus, Tzav is part of the "Torah of Aaron," which is most relevant for a person who might sin. Therefore the Chatat and the Asham come before the Shelamim, because before a person has atoned for his sins there is a suspicion that he will not sacrifice a Shelamim with a proper intention, in the name of heaven.
Source: "AS SHABBAT APPROACHES" – a biweekly column in Shabbat B'Shabbato, Vayikra 5774, Volume 1515. (Zomet Institute) See: www.zomet.org.il/eng