This may sound shocking to you, but even Satan's demons/minions believe Jesus died on a Roman gibbet two thousand years ago. Does that mean they are saved? Hardly. See James 2:19, where James does not speak of Christ's death, but he does indicate the demons are sentient beings who know what the score is regarding the Christian faith, and the "author and finisher" of our faith.
". . . fixing our eyes on Jesus, the author and perfecter of faith, who for the joy set before Him endured the cross, despising the shame, and has sat down at the right hand of the throne of God" (Hebrews 12:2 NAS).
As "timf" observed, above, an intellectual belief is one thing; a belief founded on unwavering trust is quite another. If I'm not mistaken, in the four Gospels there was a distinction made between those who
believed Christ
and those who
believed in Christ
Trusting Jesus to be one's Savior from sin, by virtue of his death, burial, and resurrection is the beginning of saving faith. What keeps us growing and maturing in faith is a regular dependence on the grace of God to keep on forgiving us when we mess up, but always on the basis of Jesus' blood and righteousness (see 1 John 1:8-10). A the hymn writer put it,
My hope is built on nothing less
Than Jesus' blood and righteousness.
I dare not trust the sweetest frame,
But wholly lean on Jesus' name.
On Christ the solid rock I stand,
All other ground is sinking sand.
All other ground is sinking sand.
