There is an important difference between worldly sorrow and godly sorrow. Worldly sorrow leads to spiritual death and sometimes it leads to physical death, too.
Godly sorrow leads to salvation and eternal life.
The apostles Peter and Paul demonstrated godly sorrow and repentance for their sins against Jesus Christ. Peter publicly denied Christ and Paul was once a persecutor of the church. Both became life-long, faithful servants of Christ. Judas, though sorrowful after he betrayed Jesus for a bribe, hanged himself. He did not seek forgiveness and allowed his great sorrow to overpower him.