There is God's salvation from sins that have been repented of through the faith of Jesus Christ (Galatians 2:20), and there is God's forgiveness of sins pre-Christ due also to faith, and through the sacrificial system that was 'time-limited' until Christ should come as the once-for-all-time perfect sacrifice for sin. Only those who had the faith God looked for, while using his sacrificial system pre-Christ, experienced the joy of God's saving grace (e.g. Abraham), with the still-future finished work of Christ on the cross applied to them. Please note, there is a difference between 'sins' (plural) and 'sin' (singular.)
In the Old Testament, when temple sacrifices had been established for God's covenant people, the difference between forgiveness and salvation can be seen when comparing king Saul with king David. Saul committed the sin of presumptuousness by taking on the role of priest for a particular sacrifice to God. This was on the back of many other sins, and culminated in him committing the sin that required death due to having consulted a witch. He died by God's decree, and was not forgiven. On the other hand, David had his own list of personal sins, yet he knew God's forgiveness and he experienced the salvation of God. Why? Because he sincerely repented and sought God's forgiveness. He got it.
Now consider another example with king David and, after his death, king Solomon. This involved a Jewish man called Shimei. The point of this protracted event, commencing with Shimei cursing king David, and not ending till many years later when Solomon notices Shimei breaking the terms of the covenant that had spared his life, is about guilt before God, and unforgiveness of such guilt.
On the day that Shimei raged against God by raging against God’s anointed, he did not die. 2 Samuel 19:18-23. His life was spared that day even though he was guilty of gross sin. Shimei, being spared his life, pursued the matter no further. Shimei did not find it impossible to live without forgiveness. He seemed to assume that, because he had escaped death that day, he had got off with it. Yet David said nothing about not imputing iniquity, and David, who wrote Psalm 32, could not live without confessing his sins to the Lord and without obtaining forgiveness, from the Lord. As expressed here:
“It seems enough for Shimei that his life is spared and that he should
continue on earth and live his life without forgiveness. But his sin
was still imputed. It still belonged to him and still lay, heavily, to
his account.
Now the days of David drew nigh that he should die, 1 Kings 2:1; and
he charged Solomon his son regarding… Shimei which had cursed him with
a strong curse in the day he went to Mahanaim. David tells Solomon
that he swore to him that he would not put him to death with the
sword. And David tells the son of David to bring Shimei’s hoar head
down to the grave with blood. For Shimei had cursed the Lord’s
anointed. 1 Kings 2:9…
Those whom God anoints, publicly, and those whom God sets forth to
speak for him, on his behalf, by prophecy (speaking as the oracles of
God) are not to be touched or harmed. To do so, interfering with the
word of God, hindering the work of God, is to invite the evident
displeasure of God Almighty.
So Solomon called for Shimei and told him to build an house in
Jerusalem and dwell there, for the day he went out and passed over
Kidron… he was to know that he would surely die. Shimei agreed with
this covenant and went his way. 1 Kings 2:36-46. But Shimei broke the
covenant which he had accepted. This covenant promised life – but only
if he kept it. He did not. And he died. For after three years Shimei
went to Gath to bring back two runaway servants. His servants meant
more to him than his life, and he paid for them with it, for Solomon
was aware of it and sent for Shimei and faced him with his covenant
breaking.
Moreover Solomon said to Shimei, ‘Thou knowest all the wickedness
which thine heart is privy to, that thou didst to David my father:
therefore the Lord shall return thy wickedness upon thine own head.’
The wickedness (ra, evil) in his heart was not brought before the
Lord that it should be forgiven and cleansed. ‘Create in me a clean
heart, O Lord,’ Psalm 51. The iniquity was still imputed. Many have a
stirring or two about their sins. But that is not the roaring that is
felt when God Almighty presses his hand down upon a man, crushing his
inner parts till he is truly humbled, really penitent, genuinely of a
broken and a contrite heart, which condition God will not despise.
So Shimei had shrugged off the iniquity which was still imputed.
Shimei had been willing to accept a covenant that depended on himself
for life. And, in due course, predictably, since his heart was
wicked, he broke it. Shimei had been granted space to repent. Time in
which to consider his ways. Days in which to meditate on a covenant
which required his obedience or, else, would require his death. But
Shimei must have had other things on his mind. His servants, for
example. Giving Solomon, wise man that he was, the just cause to do as
David required.
Shimei’s iniquity was still imputed. And Shimei died, unforgiven by
the King, under the righteous judgment of the King. In those days,
of course, God had a kingdom on earth under which men could execute
such judgments, physically, on his behalf. Now, they occur in other
ways. Upon those who blaspheme in such a way that Divine intervention
is appropriate, it will fall. Those who harm the prophets of the Lord
will be removed out of the way. Let men fear the Lord, and let men
tread carefully when he speaks upon the earth.” Righteousness,
Nigel Johnstone, pp.57-61, 2012, http://www.belmontpublications.co.uk
(Bold emphasis mine.)
The examples provided above demonstrate the difference between salvation and forgiveness (of sin) in the Old Testament.