Jamieson, Fausset and Brown on 1 Corinthians 12:12-13

12-13. Unity, not unvarying uniformity, is the law of God in the world of grace, as in that of nature. As the many members of the body compose an organic whole and none can be dispensed with as needless, so those variously gifted by the Spirit, compose a spiritual organic whole, the body of Christ, into which all are baptized by the one Spirit.

of that one body--Most of the oldest manuscripts omit "one."

so also is Christ--that is, the whole Christ, the head and body. So Psa 18:50, "His anointed (Messiah or Christ), David (the antitypical David) and His seed."