1 Corinthians 12:13 - Matthew Poole's English Annotations on the Holy Bible

The apostle proveth the oneness of the church, as the body of Christ, from the same sacraments of the New Testament instituted for all Christians, and wherein they jointly partake. He saith, we are baptized into one body, by which he must mean the universal church, for Christ is the Head of that; particular churches are but parts of that church, of which Christ is the Head. Let men be of what nation they will, whether Jews or Gentiles, turning to the Christian religion, and of what condition they will, when they are baptized they are by it made members of that one body, of which Christ is the Head; though for the more convenient administration of, and participation in, the ordinances, they are divided into smaller societies, which also have the denomination of churches; as the smallest drop of water may be called water, though there be but one element of water. And, saith the apostle, we have been all made to drink into one Spirit; which some interpret as if it were, we have all drank of one Spirit, that is, been made partakers of one Spirit, whose benefits are, sometimes set out under the notion of water, living water, 1 Thessalonians 4:10,14 1 Thessalonians 7:38,39; and so in the Old Testament, Isaiah 12:3 Ezekiel 47:1-23. But many others choose rather to interpret drinking in this place, of drinking at the table of the Lord, partaking of that whole action being set out here by one particular act there performed. This is probable, considering that the apostle, in the former part of the verse, had been speaking of the other sacrament of the gospel, and that he, speaking of the Lord's supper. 1 Corinthians 10:17, had used this expression: For we being many, are one bread, and one body.