Adam Clarke on 1 Corinthians 12:12

For as the body is one - Though the human body have many members, and though it be composed of a great variety of parts, yet it is but one entire system; every part and member being necessary to the integrity or completeness of the whole.

So also is Christ - That is, So is the Church the body of Christ, being composed of the different officers already mentioned, and especially those enumerated, 1Cor 12:28, apostles, prophets, teachers, etc. It cannot be supposed that Christ is composed of many members, etc., and therefore the term Church must be understood, unless we suppose, which is not improbable, that the term Ὁ Χριστος, Christ, is used to express the Church, or whole body of Christian believers.