The "waving" was the more solemn process of the two: it was a movement several times repeated, while "heaving" was simply a "lifting up" once.

The breast of the wave-offering, and the shoulder of the heave-offering - As the wave-offering was agitated to and fro, and the heave-offering up and down, some have conceived that this twofold action represented the figure of the cross, on which the great Peace-offering between God and man was offered in the personal sacrifice of our blessed Redeemer. Had we authority for this conjecture, it would certainly cast much light on the meaning and intention of these offerings; and when the intelligent reader is informed that one of the most judicious critics in the whole republic of letters is the author of this conjecture, viz., Houbigant, he will treat it with respect. I shall here produce his own words on this verse:

Hic distinguuntur, תנופה et תרומה, ut ejusdem oblationis caeremoniae duae. In תנופה significatur, moveri oblatam victimam huc et illuc, ad dextram et ad sinistram. In תרומה sursum tolli, et sublatam rursus deprimi; nam pluribus vicibus id fiebat. Rem sic interpretantur Judaei; et Christianos docent, quanquam id non agentes, sic adumbrari eam crucem, in quam generis humani victima illa pacifica sublata est, quam veteres victimae omnes praenunciabant.

"The heave-offering and wave-offering, as two ceremonies in the same oblation, are here distinguished. The wave-offering implies that the victim was moved hither and thither, to the right hand and to the left; the heave-offering was lifted up and down, and this was done several times. In this way the Jews explain these things, and teach the Christians, that by these acts the cross was adumbrated, upon which that Peace-offering of the human race was lifted up which was prefigured by all the ancient victims."

The breast and the shoulder, thus waved and heaved, were by this consecration appointed to be the priests' portion for ever; and this, as Mr. Ainsworth piously remarks, "taught the priests how, with all their heart and all their strength, they should give themselves unto the service of the Lord in his Church." Moses, as priest, received on this occasion the breast and the shoulder, which became afterwards the portion of the priests; see Exodus 29:28, and Leviticus 7:34. It is worthy of remark, that although Moses himself had no consecration to the sacerdotal office, yet he acts here as high priest, consecrates a high priest, and receives the breast and the shoulder, which were the priests' portion! But Moses was an extraordinary messenger, and derived his authority, without the medium of rites or ceremonies, immediately from God himself. It does not appear that Christ either baptized the twelve apostles, or ordained them by imposition of hands; yet, from his own infinite sufficiency, he gave them authority both to baptize, and to lay on hands, in appointing others to the work of the sacred ministry. Exodus 29:29

And thou shall sanctify the breast of the wave offering,.... Set it apart for the use of the priest in all succeeding ages:

and the shoulder of the heave offering: as the breast was waved from one hand to another, or cast from the hand of one to the hand of another; the shoulder was heaved up, or cast up and caught again: this also was to be sanctified or set apart for the priest's use, Leviticus 7:32,

which is waved, and which is heaved up of the ram of the consecration: the breast was waved and the shoulder heaved:

even of that which is for Aaron, and of that which is for his sons; as these two parts before mentioned in peace offerings were.

And thou shalt sanctify the breast of the wave offering, and the shoulder of the {i} heave offering, which is waved, and which is heaved up, of the ram of the consecration, even of that which is for Aaron, and of that which is for his sons:

(i) So called because it was not only shaken to and fro, but also lifted up.

29:1-37 Aaron and his sons were to be set apart for the priest's office, with ceremony and solemnity. Our Lord Jesus is the great High Priest of our profession, called of God to be so; anointed with the Spirit, whence he is called Messiah, the Christ; clothed with glory and beauty; sanctified by his own blood; made perfect, or consecrated through sufferings, Heb 2:10. All believers are spiritual priests, to offer spiritual sacrifices,