A while back, I preached on King Saul's false repentance. Dr. Bryan Chapell sums up the difference between true and false repentance well here:
"False repentance is less concerned with the spiritual contamination of sin than it is with the personal consequences of sin. True repentance is chiefly concerned with the wrong we have done to our Savior and to others. Repentance of the first kind is self-preoccupied; true repentance is a selfless seeking of spiritual fellowship and renewal. False repentance flees correction; true repentance seeks it."
Chapell, Bryan (2003-02-10). Holiness by Grace (pp. 79-80). Good News Publishers. Kindle Edition.