Conviction is the state of being convinced of error. It is the state of being convinced; a strong persuasion or belief of one's guilt. Conviction is a compelling of admission of a Truth. Conversion is a change of character, form ,or function. Believers in Christ Jesus, after conviction, experience a spiritual change from sinfulness to righteousness.
No Conviction, No Conversion!
Spiritual conversion is not a work of the flesh. In other words one cannot make himself righteous in God's eyes. God will have nothing to do with the works of the flesh,"For all have sinned, and come short of the glory of God (Romans 3:23). Spiritual conversion is man being born again "That which is born of the flesh is flesh; and that which is born of the Spirit is spirit (John 3:6). Man must repent.
"And Cain said unto the Lord, My punishment is greater than I can bear (Genesis 4:13). Cain did not see the enormity of his sin, only the severity of the punishment to come. Cain never repented; he wasn't convicted of his sin against God.
True repentance comes from a spirit of deep sorrow; a contrite spirit, one that convinced, and sincerely remorseful of his sins against God. It is recognizing the enormity of one's sin against God, not just pleading for forgiveness to lighten the consequence or rather punishment that comes with the offense.
Repent! No Conviction, No Conversion!