The following are the Greek words for "Believe," "Faith," & "Obey," with their meanings and definitions. Source of information: Vine's Expository Dictionary of New Testament Words.

A. Verbs.
1. pisteuo (Strong's 4100), "to believe," also "to be persuaded of," and hence, "to place confidence in, to trust," signifies, in this sense of the word, reliance upon, not mere credence. It is most frequent in the writings of the apostle John, especially the Gospel. He does not use the noun. Of the writers of the Gospels, Matthew uses the verb ten times, Mark ten, Luke nine, John ninety-nine times.

pistis (Strong's 4102) The main elements in "faith" in its relation to the invisible God, as distinct from "faith" in man, are especially brought out in the use of this noun and the corresponding verb, pisteuo; they are

1. a firm conviction, producing a full acknowledgement of God's revelation or truth, e. g., 2 Thessalonians 2:11‑12;
2. a personal surrender to Him, John 1:12;
3. a conduct inspired by such surrender, 2 Corinthians 5:7.

Prominence is given to one or other of these elements according to the context. All this stands in contrast to belief in its purely natural exercise, which consists of an opinion held in good "faith" without necessary reference to its proof.

"Peitho (obey) and pisteuo (believe or faith), 'to trust,' are closely related etymologically; the difference in meaning is that the former implies the obedience that is produced by the latter, cf. Hebrews 3:18‑19, where the disobedience of the Israelites is said to be the evidence of their unbelief. Faith is of the heart, invisible to men; obedience is of the conduct and may be observed. When a man obeys God he gives the only possible evidence that in his heart he believes God. Of course it is persuasion of the truth that results in faith (we believe because we are persuaded that the thing is true, a thing does not become true because it is believed), but peitho (obey), in NT suggests an actual and outward result of the inward persuasion and consequent faith."