There are two Verbs, two Nouns, and one Adjective to be considered in connection with this subject.

I.  VERBS.

1.  pisteuo = to have faith (pistis) in; hence to believe.  Translated "believe", except in eight instances, see below (iv).

i.  Used absolutely :  Matt. 8:13; 21:22; 24:23, 26.  Mark 5:36; 9:23, 24; 13:21; 15:32; 16:16, 17.  Luke 1:45; 8:12, 13, 50; 22:67.  John 1:7, 50; 3:12-18; 4:41, 42, 48, 53; 5:44; 6:36, 64; 9:38; 10:25, 26; 11:15, 40; 12:39, 47; 14:29; 16:31; 19:35; 20:8, 25, 29-31.  Acts 2:44; 4:4, 32; 5:14; 8:13, 37; 11:21; 13:12, 39, 48; 14:1; 15:5, 7; 17:12, 34; 18:1-8, 27; 19:2, 18; 21:20, 25; 26:1-27.  Rom. 1:16; 3:22; 4:11; 10:4,10; 13:11; 15:13.  1Cor. 1:21; 3:5; 14:42; 15:2, 11.  2Cor. 4:13.  Gal. 3:22.  Eph. 1:19.  1Thess. 1:7; 2:10, 13.  2Thess. 1:10.  1Tim. 3:16.  Heb. 4:3.  Jas. 2:1-19.   1Pet. 2:7.  Jude 5.

ii.  With dative of person or thing believed :  Matt. 21:25, 32; 27:42.  Mark 11:31; 16:13, 14.  Luke 1:20; 20:5.  John 2:22; 4:21, 50; 5:24, 38, 46, 47; 6:30; 8:31, 45, 46; 10:37, 38; 12:38; 14:11.  Acts 8:12; 13:41; 16:34; 18:8-; 24:14; 26:27; 27:25.  Rom. 4:3; 10:16.  Gal. 3:6.  2Thess. 2:11,12.  2Tim. 1:12.  Titus 3:8.  Jas. 2:23.  1John 3:23; 4:1; 5:10.

iii.  With direct object of the fact believed, either a Noun in the Acc. Case, or a sentence :  Matt. 9:28.  Mark 11:23, 24.  John 4:21; 6:69; 8:24; 9:18; 10:38; 11:26, 27, 42; 13:19; 14:10, 11; 16:27, 30; 17:8, 21; 20:31.  Acts 8:37; 9:26; 15:11.  Rom. 6:8; 10:9; 14:2.  1Cor. 11:18; 13:7.  1Thess. 4:14.  Heb. 11:6.  Jas. 2:19.  1John 4:16; 5:1, 5.

iv.  Translated "commit" :  Luke 16:11.  John 2:24. (both followed by Dative and Accusative);  "committed to", or "put in trust with" (Passive) :  Rom. 3:2.  1Cor. 9:17.  Gal. 2:7.  1Thess. 2:4.  1Tim. 1:11.  Tit. 1:3.

v. With Prepositions:
    (i)  eis (Ap. 104. vi) :  Matt. 18:6.  Mark 9:42.  John 1:12; 2:11, 23; 3:15, 16, 18, 36; 4:39; 6:29, 35, 40, 47; 7:5, 31, 38, 39, 48; 8:30; 9:35, 36; 10:42; 11:25, 26, 45, 48; 12:11, 36, 37, 42, 44, 46; 14:1, 12; 16:9; 17:20.  Acts 10:43; 14:23; 19:4.  Rom. 10:14.  Gal. 2:16.  Phil. 1:29.  1Pet. 1:8, 21.  1John 5:10, 13.
    (ii)  en (Ap. 104. viii) :  Mark 1:15.  Eph. 1:13.
    (iii)  epi (Ap. 104. ix) :
        1.  With Dative :  Luke 24:25.  Rom. 4:18; 9:33; 10:11.  1Tim. 1:16.  1Pet. 2:6.
        2.  With Acc. :  Acts 9:42; 11:17; 16:31; 22:19.  Rom. 4:5, 24.

vi.  In two instances, through the object being a Relative Pronoun, and attracted to the case of its  antecedent, the Verb is followed by a Genitive :  Rom. 4:17; 10:14.

There are only 248 occurrences of the Verb pisteuo (of which 99 are found in John's Gospel), but in two cases besides those noted in iv, it is followed by a direct object of the thing believed, as well as a Dative of the person.  These are John 4:21; 14:11-, and are therefore noted under both ii and iii.

2.  peitho, which is found 55 times, means to "persuade", and is so translated in Matt. 27:20; 28:14.  Luke 16:31; 20:6.  Acts 13:43; 14:19;  8:4; 19:8, 26; 21:14; 26:26, 28; 28:23.  Rom. 8:38; 14:14; 15:14.  2Cor 5:11.  Gal. 1:10.  2Tim. 1:5, 12.  Heb. 6:9; 11:13.

The Passive, "to be persuaded" or the Middle, "to persuade oneself", is translated "believe" in Acts 17:4; 27:11; 28:24.

"Obey" in Acts 5:36, 37.  Rom. 2:8.  Gal. 3:1; 5:7.  Heb. 13:17.  James 3:3;  "agreed" in Acts 5:40; and "yield" in Acts 23:21.

In Acts 12:20, the active is rendered "made ... friend", and in 1John 3:19 "assure".

peitho has a Middle Perfect, pepoitha, with a reflective sense, "I have persuaded myself" :  i.e. "I trust".  This is rendered "trust", "have confidence", &c., in Matt. 27:34.  Mark 10:24.  Luke 11:22; 18:9.  Rom. 2:19.  2Cor. 1:9; 2:3; 10:7.  Gal. 5:10.  Phil. 1:6, 14, 25; 2:24; 3:3, 4.  2Thess. 3:4.  Philem. 21.  Heb. 2:13; 13:18.

1.  pistis (*1) = faith.  The living, Divinely implanted principle.  It connects itself with the second Aorist of peitho (I. 2, above), Gr. epithon, occurs 242 times, and is always translated "faith", except in Acts 17:31, "assurance";  Titus 2:10, "fidelity"; and Rom. 3:26, and Heb. 10:39, where "of faith" is rendered "him which believeth", and "them that believe".

2.  pepoithesis = confidence.  It is derived from the Middle Perfect of peitho (I. 2, above), which is always to be distinguished from the Passive Perfect (pepeismai).  The latter refers to persuasion wrought from without; the former refers to a persuasion realized from within, and this is what pepoithesis seems to always mean.  Pistis (No. 1) refers rather to the principle, and pepoithesis refers more to the feeling.  It occurs 6 times, and is rendered "confidence" in 2Cor. 1:15; 8:22; 10:2.  Eph. 3:12.  Phil. 3:4; and "trust" in 2Cor. 3:4.

pistos occurs 67 times, and is rendered "faithful" 54 times.  It is necessary to give the references, as it is the only word so translated.  It is translated "sure" in Acts 13:34, "true" in 2Cor. 1:18.  1Tim. 3:1, and 10 times "believer", "he that believeth", &c. :  viz. John 20:27.  Acts 10:45; 16:1.  2Cor. 6:15.  1Tim. 4:3, 10, 12; 5:16; 6:2.