"'This also is yours, the offering of their gift, even all the wave offerings of the sons of Israel; I have given them to you and to your sons and daughters with you as a perpetual allotment. Everyone of your household who is clean may eat it." Numbers 18:11 NASB, bolls.life/NASB/4/18/11
There seems to have been a classification of these offerings per this online article.
The Heave Offering receives its name from the motion used in its presentation where the priest used an up and down motion–lifting it up to the Lord and receiving it back from Him.
Likewise, the Wave Offering receives its name from the motion used when the priest presented the Wave Offering in a waving type motion. The sacrifice was held in the offerer’s hands, with the priest’s hands underneath the offerer’s, and it was waved forward toward the altar and then backward from the altar–giving it to the Lord and then receiving it back from Him as a gift to the priest.
The right shoulder, better translated right thigh, of the sacrificial animal was a Heave Offering and the breast-piece was a Wave Offering. Both of these pieces were given to the priest to eat, and the rest of the flesh was given to the offerer to eat, sharing it with his family and friends in the presence of the Lord in His sanctuary.
The Heave and Wave Offerings were part of the Peace Offering, which was one of the five Offerings we read about in the book of Leviticus. (The five types of Levitical Offerings were the Burnt Offering, the Meat Offering, the Peace Offering, the Sin Offering, and the Trespass Offering.)
The Peace Offering was the only offering in which the donor received back a portion of the sacrifice to eat himself. Furthermore, it was the only animal sacrifice that did not deal with making atonement for sin. The Meat Offering was the only Offering of the five that did not involve an animal sacrifice–it was a Meal or Cereal Offering instead of an animal sacrifice.