John Nelson Darby emphasizes the distinction between the true Church and the broader profession of Christianity in his sermon on 1 Corinthians 1. He highlights that while all who call upon the name of Jesus are treated as Christians, there is a critical difference between being part of the Church, called saints, and merely professing faith. Darby points out that the Apostle Paul addresses the Corinthians as the Church of God, acknowledging their gifts while also preparing to correct their errors. He stresses the importance of recognizing Christ's Lordship and the responsibility that comes with being part of the Church, especially in light of the challenges faced by the early Christians. The sermon serves as a reminder of the need for discernment in the faith community and the ongoing relevance of these principles today.