In Calvin’s thinking, the signs of the sacraments should be distinguished from the realities which they signify, but they should not be separated from them. First Corinthians 10:1-4 says,
For I do not want you to be unaware, brothers, that our fathers were all under the cloud, and all passed through the sea, and all were baptized into Moses in the cloud and in the sea, and all ate the same spiritual food, and all drank the same spiritual drink. For they drank from the spiritual Rock that followed them, and the Rock was Christ.
In Calvin’s commentary on this text, the Reformer makes the following observations about the signs and realities of the sacraments.
When [Paul] says that the fathers ate the same spiritual meat, he shows, first, what is the virtue and efficacy of the Sacraments, and, secondly, he declares, that the ancient Sacraments of the Law had the same virtue as ours have at this day. For, if the manna was spiritual food, it follows, that it is not bare emblems that are presented to us in the Sacraments, but that the thing represented is at the same time truly imparted, for God is not a deceiver to feed us with empty fancies.
A sign, it is true, is a sign, and retains its essence, but, as Papists act a ridiculous part, who dream of transformations, (I know not of what sort,) so it is not for us to separate between the reality and the emblem which God has conjoined. Papists confound the reality and the sign: profane men, as, for example, Suenckfeldius, and the like, separate the signs from the realities. Let us maintain a middle course, or, in other words, let us observe the connection appointed by the Lord, but still keep them distinct, that we may not mistakenly transfer to the one what belongs to the other.
So Roman Catholics err by confounding the reality and the sign. Anabaptists err by separating them. Calvin argues that sign and reality must be kept distinct, but they must not be severed.
The sacraments are signs, but they are not empty or bare signs, nor are they signs of something absent but of something present, given, and received.
Ultimately, the reality signified by the signs is Jesus Christ himself and all the benefits of redemption which are found in him.