As this passage shows, the Passover lamb did much more than just provide blood - it was a distinctive meal. God begins with instructions to ensure that every person would have enough, but also that it would not be wasted. He continues with specific details, including when it should be eaten, how it should be prepared, what should be eaten with it, what should be done with the remains, and even how the Israelites should be dressed. The bulk of God's instructions concern the specially prepared lamb they were to eat. The repeated emphasis in both Old and New Testaments is on the eating of the Passover (Exodus 12:43, 48; 34:25; Numbers 9:11; II Chronicles 30:18; Ezra 6:21; Matthew 26:17, 26; Mark 14:12, 14, 22; Luke 22:8, 11, 15, 19; John 13:2; I Corinthians 11:23-26; see John 6:31-58), and this begins to set it apart from a sin offering, which was not generally available for eating.
A second difference is who was allowed to eat each sacrifice. The Passover was a meal shared by a circumcised household, while in the sin offering, only the males among the priests ate portions of it (Leviticus 6:26), and only in two cases. The sin offering is divided into four categories, according to who had committed the sin, whether a priest (verses 3-12), the whole congregation (verses 13-21), a leader of the people (verses 22-26), or an individual (verses 27-31). In the case of a priest or the whole congregation, the priest offered part of the animal on the altar as God's portion, and then he burned the remainder outside the camp (Leviticus 4:8-12, 19-21; 6:30), and thus, nothing was eaten by the priest. The priests could only eat a sin offering for a leader or another individual.
This teaches that while the priest could receive a portion for his service in performing the work of the sin offering in some cases - that is, when the offering was for the sin of a leader or other individual - he could not receive any portion when it was for the sin of the priesthood or the congregation, of which he was a part. In other words, he was not to eat of the offering for sins he had a part in. In addition, God did not allot any of the sin offering for the one making the offering. When we apply this to the Passover, it gives us a third reason why it was not a sin offering: In type, it would signify each household benefitting from - being fed by - the sins they had committed, which is entirely contrary to the divine pattern.
As mentioned, only the priests could eat of the sin offering, and only when it was for a leader or an individual (other than a priest). Of the four scenarios, a household (being a group) is the most like a congregational offering, and in that scenario, none of the sacrifice was to be eaten. What wasn't put on the alter was burned outside the camp.
That clearly instructs the Israelites to use a male lamb or a male kid of the goats from their flocks only. Note that it says male kid, and not the herd. If we take the word that is given in Deuteronomy 16:2, where it says "the flock and the herd," it would then be possible to have a Passover calf. That word there translated into English "herd" is baqar. That word means "bovine" in English.
Remember this in contrast to the Passover. It always had to be something from the flock—a lamb or a goat. You never heard of a Passover calf. Jesus Christ was not the Passover calf slain from the foundation of the world.
Notice the phrase "at the place which the LORD your God shall choose." This clearly contradicts Exodus 12 and Numbers 9 which command a domestically-killed Passover lamb.
Beginning in Exodus 25 we saw all the instructions for the building of the Tabernacle, for the making of the dress of the priests, for all of the furniture, for all of the appurtenances of the Tabernacle, and the consecration of both the priests and the Levites. All of this was given by command in the first month of the second year of the coming out of Egypt. We saw the completion in the story of the Tabernacle, and then the first thing they did was keep a Passover. That is recorded in Numbers 9. There was no change between Exodus 12 and Numbers 9, even though now the Tabernacle existed and the priesthood was installed and consecrated and in its place.
A domestically-killed Passover lamb was still the command after the Temple and the priesthood were in place. This makes it very clear these things that were offered at the Tabernacle, or the Temple, were not the Passover lamb. They were other offerings. That is six differences, with Exodus 12, Numbers 9, Leviticus 23, or Leviticus 33.
