Conviction comes before repentance, but is not repentance itself. No one repents unless they are convicted, but not all who are convicted actually repent. Repentance is not just worldly sorrow. Some people are very sorry because of the consequences of their sin, or because they have been caught. Many people are sorry, not for what they have done wrong, but for the penalty they receive in being caught.
Many people try in their own strength to become a better person and change their way of life.
Repentance is not becoming religious. The Pharisees were extremely religious in behavior and practice. They fasted and prayed and had many religious ceremonies, yet never repented. Repentance is not just mental acceptance of truth. Having an intellectual head-knowledge of truth does not necessarily guarantee that the truth has become a living reality in one's life.