What is the difference between an offering and a sacrifice? The terms are important to distinguish.
Offering (minha) is the broader category. It refers generally to anything brought to the cultic establishment as a donation to the deity and (indirectly) to the priestly personnel.
Sacrifice (zevach; the same word is used for feast in 1 Samuel 20:29) refers only to offerings that are burned in fire, either totally or partially.
There is a high degree of interconnection, however, among the various terms used for sacrifices and offerings, which greatly complicates the categorization process.
An offering can simply be a gift or a tribute. In a cultic context, it is primarily a cereal offering. Since most people in ancient Israel were agriculturalists, most tithes and offerings given to the sanctuary were in the form of cereal offerings. So, the routine term for bringing gifts to be dedicated to the deity (and eaten by the priests and Levites) eventually was associated only with cereal offerings. The cereal offering, even though it belongs in a separate category from animal sacrifices, is nevertheless often paired with the burnt offering (Hebrew ‘ola) because it functioned as the poor person’s equivalent to the burnt offering. The interlinking motifs among these various terms for sacrifices and offerings reveal the highly complex and nuanced nature of these cultic traditions.
Perhaps the earliest list of sacrifices in the Bible appears in Amos, where God rejects the sacrifices performed by the prophet’s hypocritical audience:
Even though you offer me your burnt offerings and grain offerings,
I will not accept them.
And the offerings of well-being of your fatted animals,