Scholars are uncertain as to the significance of the occasional differentiation between shelamim and zevaḥ in the Biblical text. In the late 19th century, a few scholars proposed that the shelamim offering was a more solemn version of the zevaḥ offering, and/or that the portion assigned allocated to God differed between them.
Slaughter offerings were also made in response to the ratification of solemn covenants, treaties, and alliances.
The fat of the animal was the portion allocated to the deity, and was burnt on the altar; the priests were allocated the breast and right shoulder, which was first waved around the altar (making this portion a wave offering); the remainder went to the offerer. The meat had to be consumed within a certain time limit; for praise offerings it had to be consumed on the day of the sacrifice, while for the other types of slaughter offering it had to be consumed by the day afterward; any leftovers had to be destroyed on the third day, outside the camp. The offerer was permitted to invite guests to consume the meal with him, along with strangers, paupers, servants, and Levites, as long as they were all ritually clean. The meals were treated as a joyful occasion, and would be accompanied with wine, as well as bread (both leavened and unleavened), oil, and salt.
However, what is generally considered the most likely explanation, is that sacrifice-of-peace offerings simply originated as meals, the consumption of which directly improved health (as opposed to starvation), and hence indirectly improved prosperity (shelamim being understood to mean prosperity/health). When sanctuaries outside Jerusalem began to be suppressed, and eventually outlawed by Josiah, the impracticality of going to Jerusalem to sacrifice an animal simply to consume meat, led to killing an animal for food gaining an independent existence from the sacrifice-of-peace offering.
The concentration of these sacrifices, the main offering given by private individuals, at a single sanctuary evidently resulted in such large numbers of offers that the space on the north side of the altar, where the animals were killed in the other types of sacrifices, became cramped, hence the specific permit for sacrifice-of-peace offerings were to be killed anywhere within the sanctuary courtyard. How exactly a portion of the resulting meat was given to God appears to have varied; though the regulations of the Priestly Code point to God's portion being burnt on the altar, Gideon is described in the Book of Judges, a text which textual scholars believe has a much earlier date than Leviticus, as pouring out broth, made from the meat of the sacrifice, as a libation.