There is a big difference between sins being "paid for" at the cross and sins being "forgiven" at the cross. ALL sins were paid for at the cross, but none were forgiven at the cross.
The ultimate sacrifice of Christ on the cross made it possible for all sins to be forgiven. But first there must be repentance toward God and faith toward our Lord Jesus Christ (Acts 20:21). Repentance is for the remission or forgiveness of sins.
That is not strictly true ... David was forgiven [Cornelius] before he even recognised his sin when confronted by Nathan.
's all by grace, yes, yes through faith but grace is before everything with God. There have been times when God winked at sin, there have been times when sin was not counted against folk.
With David it is important to note that his sin did not go unpunished ... his life was full of sorrows after Bathsheba.
Repentance is simply to change mind and heart, to turn around.
When we's out preaching when people stop and listen and take interest they are repenting, when people turn their thoughts toward God and consider His claims upon them.
if at that point you throw the word "repent" [and even wuss "repent or be damned"] it just throws them. Rather simply call upon them to BELIEVE and RECIEVE and if at all possible lead them in prayer.
Sorrow for sin often comes after we are saved, sometimes a long time after.