A real change of heart brings about an active belief.
Rom. 10:8 But what does it say? “The word is near you; it is in your mouth and in your heart,” that is, the word of faith we are proclaiming:
Rom. 10:9 That if you confess with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved.
Rom. 10:10 For it is with your heart that you believe and are justified, and it is with your mouth that you confess and are saved.
These definitions are from the N.I. Bible Dictionary
CONVICTION (Gr. elencho, to convince or prove guilty). Conviction is the first stage of repentance, experienced when in some way the evil nature of sin has been brought home to the penitent, and it has been proved to him that he is guilty of it. Although the word “conviction” is never used in KJV, both Testaments give many illustrations of the experience. In the OT one of the most notable is found in Psalm 51, where David, realizing he has sinned against God, is overwhelmed with sorrow for his transgression and cries out to God for forgiveness and cleansing. In the NT the central passage bearing on this theme is John 16:7-11, where Jesus says that when the Holy Spirit comes “he will reprove the world of sin, and of righteousness, and of judgment” (kjv). Here the word “reprove” (niv “convict”) means “convince” (so rsv) or “prove guilty.” The thought is that the Holy Spirit addresses the heart of the guilty and shows how inadequate ordinary standards of righteousness are. The purpose of conviction is to lead to godly repentance.
REPENTANCE (Heb. naham, subh, Gr. metanoia). The process of changing one’s mind. In the KJV of the OT God himself is described as repenting (Exod 32:14; 1 Sam 15:11; Jonah 3:9-10; 4:2—using naham), in the sense that he changed his attitude to a people because of a change within the people. God as perfect Deity does not change in his essential nature; but because he is in relationship with people who do change, he himself changes his relation and attitude from wrath to mercy and from blessing to judgment, as the occasion requires. His change of mind is his repentance, but there is no suggestion of change from worse to better or bad to good. In contrast, human repentance is a change for the better and is a conscious turning from evil or disobedience or sin or idolatry to the living God (2 Kings 17:13; Isa 19:22; Jer 3:12, 14, 22; Jonah 3:10—using shubh).
In the NT repentance and faith are the two sides of one coin (Acts 20:21). They are a response to grace. Jesus preached the need for the Jews to repent (Matt 4:17), and required his apostles/disciples to preach repentance to Jews and Gentiles (Luke 24:47; Acts 2:38; 17:30). Repentance is a profound change of mind involving the changing of the direction of life from that of self-centeredness or sin-centeredness to God- or Christ-centeredness. God’s forgiveness is available only to those who are repentant, for only they can receive it.
The positive side of repentance is conversion, the actual turning to God or Christ for grace. This is conveyed in the NT by the noun epistrophe (once only, in Acts 15:3) and the verb epistrepho (e.g., Acts 15:19; 2 Cor 3:16). The difference between metanoia and epistrophe and metanoeo and epistrepho is only one of emphasis, for a full repentance is truly a conversion.
CONVERSION (Heb. shuv, Gr. epistrophe). The words commonly used in the English Bible as equivalent to the Hebrew and Greek words are “turn,” “return,” “turn back,” “turn again.” Thus conversion is synonymous with “turning.” The turning may be in a literal or in a figurative, ethical, or religious sense, either from God or, more frequently, to God. It is significant that when the turning refers to a definite spiritual change, it almost invariably denotes an act of man: “Turn! Turn from your evil ways!” (Ezek 33:11; cf. Matt 18:3). Since the word implies both a turning from and a turning to something, it is not surprising that in the NT it is sometimes associated with repentance (Acts 3:19; 26:20) and faith (11:21). That is, conversion on its negative side is turning from sin and on its positive side is faith in Christ (“they must turn to God in repentance and have faith in our Lord Jesus,” 20:21). Although conversion is an act of man, Scripture makes clear that it has a divine ground. The turning of sinful people is done by the power of God (3:26). In the process of salvation, conversion is the first step in the transition from sin to God. It is brought about by the Holy Spirit operating on the human mind and will, so that the course of one’s life is changed. It is not the same as justification and regeneration, which are purely divine acts. It may come as a sudden crisis or as a more or less prolonged process.
SANCTIFICATION (Gr. hagiasmos from the verb hagiazo). The process or result of being made holy. As the article on HOLINESS makes clear, holiness when applied to things, places, and people means that they are consecrated and set apart for the use of God, who is utterly pure and apart from all imperfection and evil. When used of people, it can refer also to the practical realization within them of consecration to God: that is, it can have a moral dimension. Thus in the NT, believers are described as already (objectively) sanctified in Christ—“your life in Christ Jesus, whom God made our sanctification” (1 Cor 1:30 rsv), and “those sanctified in Christ Jesus” (1:2). Also, though set apart in Christ for God and seen as holy by God because they are in Christ, believers are called to show that consecration in their lives—“It is God’s will that you should be sanctified” (1 Thess 4:3), and “May…the God of peace sanctify you” (5:23). The same emphasis is found in Hebrews (2:11; 9:13; 10:10, 14, 29; 13:12). Because believers are holy in Christ (set apart for God by his sacrificial, atoning blood), they are to be holy in practice in the power of the Holy Spirit. They are to be sanctified because they are already sanctified.