Under the OT, they "Sacrificed animals" and their sins were FORGIVEN
But note what Hebrews says about this.
Heb 10:4 For it is not possible that the blood of bulls and of goats should take away sins.
So, What's the difference between "FORGIVEN" and TAKEN AWAY" sin???
Forgiven, doesn't "PAY THE WAGES OF SIN".
Ro 6:23 For the wages of sin is death;
"DEATH" is the only thing that will pay those wages or "TAKE AWAY" sin.
Jesus is only dying "ONCE" to "TAKE AWAY" sin, and in that ONCE, he paid for the sins of the "WHOLE WORLD", Adam/Eve to the last person saved who believes.
Where you, and many other, make a mistake is "THINKING" that a sin committed "AFTER" being saved is simply "FORGIVEN" without anyone having to "DIE" to pay the wages of that sin.
It doesn't work like that, the wages of "EVERY SIN" must be paid by a "DEATH", the "LAW" requires it.
Mt 5:18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
"Forgiven sin"= is sin "TRANSFERRED TO JESUS" for "PAYMENT".
"TAKEN AWAY SIN"= Wages of sin "PAID", Jesus's death.
Joh 1:29 The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which....taketh away.... the sin of the world.
The "WAGES" of every sin will be paid by a "DEATH", either Jesus or the person.
Once saved, You CAN'T" commit a sin Jesus hasn't "ALREADY" paid for. OSAS
Catholic's work so people in "purgatory", are "FORGIVEN" of their sin, but God "NEVER FORGIVES" the "WAGES OF SIN", even one, that is a "DEBT" that must be "PAID".
Jas 2:10 For whosoever shall keep the whole law, and yet offend in one point, he is guilty of all.
You're saved "FOREVER" by Jesus's death, or "NOT AT ALL".