The Judgment Seat of Christ is for the saved, while the Great White Throne judgement is for unsaved. However, that doesn't necessarily mean these are two separate events.
Judgment Seat of Christ
2 Corinthians is written to believers; Paul opens the letter with "Paul...Unto the church of God which is at Corinth". In chapter 5 Paul exhorts the Corinthians to labor for Christ, telling them that "we must all appear before the judgment seat of Christ." Paul goes on to say that the judged will receive what is due them, depending on the works they did on earth. The Judgement Seat of Christ is also referenced in 1 Corinthians:
1 Corinthians 3:10-15 (KJV)
...I have laid the foundation, and another buildeth thereon. But let every man take heed how he buildeth thereupon. For other foundation can no man lay than that is laid, which is Jesus Christ. Now if any man build upon this foundation gold, silver, precious stones, wood, hay, stubble; Every man's work shall be made manifest: for the day shall declare it, because it shall be revealed by fire; and the fire shall try every man's work of what sort it is. If any man's work abide which he hath built thereupon, he shall receive a reward. If any man's work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire.
These passages reveal that the Judgement Seat of Christ is when Christians will be judged for the works they did after they accepted salvation.
Great White Throne Judgment
Revelation 20:12 (KJV)
And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
Here the dead are judged "according to their works," like the Judgment Seat of Christ.
Revelation 20:13, 15 (KJV)
And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works...And whosoever was not found written in the book of life was cast into the lake of fire.
So the unsaved are definitely judged at the Great White Throne Judgment.
The saved are present at the Judgement Seat of Christ, and the unsaved are present at the Great White Throne Judgment. Is it possible that they take place at the same time? Yes. Both judgments are a judgment of earthly works. It could be that Paul and John just chose to focus on different aspects of the same event.
It is also possible that these judgments take place at different times. Nothing in scripture prevents them from occurring separately, and they are certainly referred to in different manners.
Ultimately, whether they take place together or not, the salient point is that both the saved and the unsaved will be judged for how they lived their lives.