Bowing profoundly, with his hands joined and placed upon the altar, he [the priest] says:
Supplices te rogamus, omnipotens Deus: jube haec perferri per manus santi Angeli tui in sublime altare tuum, in conspectu divinae majestatis tuae: ut quotquot [he kisses the altar] ex hac altaris participatione sacrosanctum Filii tui [he joins his hands, and signs the Host and then the chalice with the Sign of the Cross] Cor+pus et San+guinem sumpserimus [he signs himself with the Sign of the Cross] omni benedictione caelesti et gratia repleamur. [He joins his hands.] Per Christum Dominum nostrum. Amen.
We must humbly beseech Thee, Almighty God, to command that these offerings be borne by the hands of Thy holy Angel to Thine altar on high in the sight of Thy Divine Majesty, that many of us as at this altar shall partake of the Body+ and Blood + of Thy Son, + may be filled with every heavenly blessing and grace. Through the same Christ our Lord. Amen.
I am not sure I understand the significance of the difference, except that it is the Holy Ghost, Who, in the Divine Economy of Our Salvation, is affecting the changes.
It is also my understanding that the TLM also contains additional prayers (from about the 13th century) that do call on the Holy Ghost.
Quam oblationem tu, Deus, in omnibus, quaesumus, benedictam, adscriptam, ratam, rationabilem, acceptabilemque facere digneris: ut nobis Corpus et Sanguis fiat dilectissimi Filii tui Domini nostri Jesu Christi.Perhaps those Orthodox theologians who would prefer to identify the Supplices as the epiclesis do so because, like the Byzantine epiclesis, it comes after the Consecration.And do Thou, O God, vouchsafe in all respects to bless, consecrate, and approve this our oblation, to perfect it and to render it well-pleasing to Thyself, so that it may become for us the Body and the Blood of Thy most beloved Son, Jesus Christ, our Lord.
It should be noted that this ambiguity does not exists in the new Eucharistic Prayers of the Novus Ordo Mass which have explicit invocations of the Holy Spirit.