Is the great white throne judgment the same as the judgment seat Christians face?
No. The great white throne is a distinct judgment reserved only for the lost and unbelievers, from Cain until the last one at the end of the ages. Christians will not be there; they face a separate judgment seat, not this great white throne.
Les explains that although Christ's atoning blood paid for all the world's sins, a lost person who spurns that payment in unbelief must still give an account for everything done in the body as a lost person. Every unbeliever from Cain until the last one at the end of the ages will come before the great white throne, as Revelation 20:12 describes the dead, small and great, standing before God. This judgment is not the bema seat that Christians will face; it is only for the lost and unbelievers. Christians will not be at the great white throne, nor will they see loved ones who may be unbelievers. The Judge there is the Lord Jesus Christ.