There are two forms of words used in the New Testament which are translated repent and repentance.
Only one of these is used of the repentance associated with salvation from sin. This is the verb metanoeo, and the corresponding noun metanoia. The other verb is metamelomai, the noun of which does not appear in the New Testament, but occurs in the Septuagint in Hosea 11:8. The verb is used in the Septuagint in Psalm 110:4; and Jer. 20:16. It is also the word used in the New Testament in Matt. 21:29, which says of the son who had refused to obey his father's command to work in the vineyard, "afterward he repented himself and went." It likewise is found in Matt. 21:32 and 27:3, this latter being the case of Judas. Paul uses it in Rom. 11:29; and 2 Cor. 7:8, 10. It is also the word used in Heb. 7:21. In all other places, translated repent and repentance in the New Testament, the original is metanoeo or metanoia. This word means to reconsider, to perceive afterwards, and hence to change one's view, mind, or purpose, or even judgement, implying disapproval and abandonment of past opinions and purposes, and the adoption of others which are different. In all cases of inward change there is not necessarily a change of outward conduct, nor is such inward change accompanied by regret. These results would flow from the nature of that about which that change has arisen.
We arrive, therefore, at the meaning of Christian repentance partly through the meaning of these Greek words, but also partly because it is exercised about a question of morals. It is seen that it involves a change in the outward life because such change is a result of the change of inward opinions. It also includes sorrow for sin because a change of view as to the nature of sin and of holiness must be accompanied by regret and sorrow as to the past acts of sin.
The word metamelomai means to change one's care, to regret; the idea of sorrow always accompanying it.
The two words are nearly synonymous in their secondary meaning, and each is used in this secondary meaning in the New Testament. Metanoeo, however, traces the feeling of sorrow and the change of life back to an inward change of opinion and judgement as to the nature of sin and holiness, and of the relations of man and God. It is perhaps on this account that it is exclusively used for true repentance in the New Testament. This is not simply sorrow, or remorse, which may pass away, or lead in despair to other sins, or fill the soul with anxiety' but a heartfelt change in the inward soul towards God and holiness, which is lasting and effective, and which may be associated with peace and joy in believing.
