Here is an extended quote from Herman Bavinck’s article on Calvin’s view of the Lord’s Supper. Bold is mine.
In a manner that is different and still clearer than in the gospel, Christ is presented to us in the Lord’s Supper as the only food for our souls. In the signs of bread and wine he himself is truly and essentially present; in the Lord’s Supper we properly receive Christ’s own body and his own blood. Through eating the bread and drinking of the cup, we become partakers not merely of the Spirit of Christ and his benefits obtained through his dying, but specifically of the proper flesh and blood of the crucified and now glorified Savior. With this objective view of the sacrament, Calvin stands decidedly on the side of Rome and the Lutherans. As vigorously as possible he opposes the notion that the Lord’s Supper is merely a confession of our faith or a remembrance of the Lord’s death. He can hardly find words strong enough to express his conviction concerning the real, essential, genuine presence of Christ’s own flesh and of his own blood in the Lord’s Supper. He declares explicitly that the issue between him and his Roman Catholic and Lutheran opponents involves only the manner of that presence.
What then is the difference? The opponents could conceive of no other fellowship with Christ and no other presence of Christ in the Lord’s Supper than a local, sensory, material presence, the kind of presence whereby the body and blood of Christ descend from heaven and are changed into or contained within the bread and wine. This kind of presence is strenuously opposed by Calvin. This is in conflict with what Holy Scripture teaches us about the truly human nature of Christ, about his ascension and glorification at the right hand of the Father. Christ is still truly human, [a humanity that is] finite, limited, governed by space and therefore located in heaven. It is wholly false when these opponents can imagine no other fellowship with Christ’s flesh and blood than one which consists in the merging of Christ with them in the same location. But that is a kind of presence that ties Christ to and contains him within the elements of bread and wine. Such a presence robs him of his greatness and majesty and glory, one that detracts from his human nature. Flesh must remain flesh, and the human must remain human. Calvin opposes this Roman Catholic and Lutheran doctrine not first of all because transubstantiation and consubstantiation are impossible, but because they detract from the genuineness and glory of Christ’s human nature.
But even though this particular manner of Christ’s presence was rejected by Calvin, he did not deny that presence itself. He gladly accepted everything that could serve to express our true and substantial fellowship with the body and blood of Christ, just as long as it was the kind of presence that did not rob Christ of his majesty. Indeed, Calvin teaches a much more genuine and much more essential presence of Christ’s flesh and blood in the Lord’s Supper than the Roman Catholics and the Lutherans. But the latter appeared unable and unwilling to grasp the nature and the manner of the presence of Christ that Calvin was teaching. And that lay in the differing meaning people attached to the word spiritual.
When Calvin opposes the physical, local presence and over against that teaches that Christ is present in the Lord’s Supper in a spiritual manner (spiritualiter), then his opponents understood him to be teaching merely a non-essential, deceptive, imaginary presence, a presence within the mind, in the imagination, in the remembrance. Calvin himself had complained of that misunderstanding already in his struggle against Westphal and Heshusius. Westphal could not distinguish between an imaginary (imaginarium spectrum) and a spiritual fellowship with Christ; and his comrades in faith suffer the same limitation to this day. For Westphal, fellowship with Christ consisted in the fact that Christ’s flesh entered his mouth and stomach. Nevertheless, the term spiritual stands in contrast not with genuine and essential, but over against physical and material.
The spiritual presence that Calvin taught is much more of an essential presence than the physical presence of the Roman Catholics and Lutherans, which by itself is wholly unprofitable. And that presence does not exist merely in the imagination or in the mind, but in the Lord’s Supper we become partakers of the proper flesh and blood of Christ in reality and in truth.