From Anstey’s Doctrinal Definitions:
This term refers to the time when Christ will be displayed with the Church in manifested glory before the world (2 Thess. 1:10; John 17:23). The “day of Christ” (or “the day of Jesus Christ”) will begin at the Appearing of Christ and will continue throughout the Millennium (1 Cor. 1:8; 3:13; 5:5; 2 Cor. 1:14; Phil. 1:6, 10; 2:16). Thus, it will last 1000 years. The day of Christ is abbreviated to “that day” in some places in Paul’s epistles (2 Thess. 1:10; 2 Tim. 1:12, 18; 4:8). The rewards which the saints will receive at the judgment seat of Christ will be on display then (1 Cor. 3:13; 2 Tim. 1:12; Phil. 2:16).
“The day of Christ” is not the day that the Lord spoke of in the upper room when He said, “In that day....” (John 14:20; 16: 23, 26). The Lord was speaking of this present day when the Spirit would come to reside on earth in the Church. Nor is it the same day that the Old Testament prophets spoke of when they said, “In that day....” (Zech. 12:3, 4, 6, 8, 9, 11; 13:1, 2, 4, etc.) which is the Messiah’s day on earth in connection with Israel. The day of Christ has to do with His heavenly glory with the Church.
“The day of Christ” and “the day of the Lord” refer to the same period of time (the Millennium); the former emphasizes the display of Christ’s glory and the latter the exercise of His judgment.