The Apostle John used the words "believe" (94 times), "trust" (3 times), and "faith" (15 times) in his Gospel, three epistles, and Revelation. In fact, his stated purpose in writing was that his readers would believe in Christ, and be saved (Jn. 20:31). During one of His post-Resurrection appearances, Jesus told Thomas, who had just addressed Jesus as "my Lord and my God," "because thou hast seen Me, thou hast believed: blessed are they that have not seen, and yet have believed" (Jn. 20:28-29). To be fair to Thomas, he was not present when Jesus "breathed on them, and saith unto them, Receive ye the Holy Ghost" (Jn. 20:22).
What did Jesus mean by "believe?" The Greek word used by John in quoting Jesus, was πιστεύω (pisteuō), which is translated "believe" 239 times. Ironically, πιστεύω is from the root, πίστις (pistis), a word translated "faith" 239 times! Even more ironic is the fact that "believe" can be defined as having "absolute knowledge" based upon the fact that Satan and his minions, having seen Jesus in His glory, believe Christ exists, but they obviously do not believe in Him. James wrote, "Thou believest that there is one God; thou doest well: the devils also believe, and tremble" (Jam. 2:19).
What is the difference in believing Christ exists and believing in Him? You might say it is the difference between have "head knowledge" and having "heart knowledge." It is how one responds to the knowledge of who He is. If one believes, or has faith in Him, and places his trust in Him as Lord, voluntarily submitting to His will, that person is born again. If one refuses to allow Him rule over him, he is like Satan.
Believing in Jesus and bowing before Him, results in eternal salvation (Jn. 3:15);
being forced to bow before Him, will result in eternal damnation (Rom. 14:11).