SB,
That's not how the grammar of
pistis and
pisteuo work in Greek. For the feminine noun,
pistis (faith),
pist indicates the main stem which we pursue to discover the
etymology of the root stem. The suffix,
is, indicates it's a singular, feminine noun.
Pist, the root of both faith and believe, comes from
peitho, which means “tried to convince” (Acts 18:4), “persuade, appeal to someone” (2 Cor 5:11), “conciliate, satisfy” (Matt 28:14), “depend on, trust in, put one’s confidence in” (Philm 21; Lk 11:22), “be convinced, be sure, certain” (Rom 2:19; Heb 13:18); in the passive voice, “be persuaded, be convinced, come to believe” (Luke 16:31; Heb 11:13); “obey, follow” (Rom 2:8; Gal 3:1); and “be convinced, certain” (Heb 6:9; Luke 20:6).
[1]
As for the verb,
pisteuo,
pist is from
peitho (see meaning above). The suffix,
euo, indicates it's a first person, present tense verb, i.e. I am continuing to believe (have faith) since the Greek verb indicates
kind of action and not primarily the
time of action.
On author summarised this with precision: "The root of
pistis ("faith") is
peithô ("to persuade, be persuaded") which supplies the
core-meaning of faith ("
divine persuasion"). It is God's warranty that guarantees the fulfillment of the revelation He births within the receptive believer (cf. 1 Jn 5:4 with Heb 11:1)" [
source].
Therefore, in my understanding, the root meaning of
pistis and
pisteuo is basically the same: "faith" and "I believe/I have faith". Both refer to "divine persuasion."
Why would John use "believe" and not "faith" in John 3:16 (NIV)? "For God so loved the world that he gave his one and only Son, that whoever
believes in him shall not perish but have eternal life." To believe leads to eternal life and saving from perishing. Romans 5:1 (NET) states, "Therefore, since we have been
declared righteous by faith, we have peace with God through our Lord Jesus Christ." I conclude faith and to believe are used interchangeably.
There is a very large article showing the similarities and differences between these words in Kittel & Friedrich's (eds),
Theological Dictionary of the New Testament, vol 6, pp. 174-228. You'll need to be able to read Greek and understand its grammar to gain full benefit from this article.
Please let me know if I need to 'clear the fog' in this explanation.
Oz
[1] Peitho’s definition is from Bauer, Arndt and Gingrich Greek Lexicon (1957, 644-45).