|John 3:16 Updated American Standard Version (UASV)
16 For God so loved the world that he gave his only-begotten Son, in order that everyone trusting in him will not be destroyed but have eternal life.
|John 3:36 Updated American Standard Version (UASV)
36 The one trusting in the Son has eternal life, but the one who disobeys the Son will not see life, but the wrath of God remains on him.
A Grammar of New Testament Greek series, by James Moulton, says, “The importance of the difference between mere belief … and personal trust.” Both these senses can be conveyed using the Greek word pisteuo. The context helps us to identify the different senses of the meaning of pisteuo. Then again, we also have the different grammatical constructions that also convey what the Bible author had meant by his use of the word. When pisteuo is simply followed by a noun in the dative case, it is merely rendered as “believe,” such as the chief priest and elders response to Jesus at Matthew 21:25, “If we say, ‘From heaven,’ he will say to us, ‘Why then did you not believe him?’ However, in Romans 4:3 we have pisteuo follow by a noun in the dative in the Updated American Standard Version, yet it is rendered “For what does the Scripture say? “Abraham put faith in God, and it was credited to him as righteousness.” (The ASV, RSV, ESV, NASB and others have “Abraham believed God”)
If pisteuo is followed by the Greek preposition epi, “on,” it can be rendered “believe in” or believe on.” At Matthew 27:42, it reads, “we will believe in him [i.e., Jesus].” At Acts 16:31, it reads “And they said, Believe on the Lord Jesus Christ, and thou shalt be saved …” (KJV, UASV similarly) What is the difference between “believing in Jesus” and “believing on Jesus”? Believing in Jesus is a merely acknowledging that he exists while believing on Jesus is to accept absolutely, having no doubt or uncertainty, trusting in, putting faith in or trust in, exercising faith in the Lord Jesus Christ.
If pisteuo is followed by the Greek preposition eis, (“into, in, among,” accusative case), it is generally rendered “trusting in” or “trust in.” (John 3:16, 36; 12:36; 14:1) The grammatical construction of the Greek verb pisteuo “believe” followed by the Greek preposition eis “into” in the accusative gives us the sense of having faith into Jesus, putting faith in, trusting in Jesus.
 James Moulton, A Grammar of New Testament Greek, Vol. 1: Prolegomena (London, England: T & T Clark International, 2006), 68.