Good question. Yes, saved in the Bible means being saved from all your sins. In fact, you should have no more sins in your heart. Your heart should be sinless if you are saved. If you still have sin then you are not saved. Many Christians who claim to be strong believers also say they still have sin??? How is this possible?? To be saved from your sins you must believe in the true gospel of the water and the Spirit. You can't be saved by just believing in Jesus somehow, that will not save you. That verse you quoted means, you must believe in everything Jesus did for your salvation. If you only take one part of His atonement like many do of just His blood on the Cross, then you will never be saved ever (1 John 5:6-11). The blood alone cannot save you from your sins, this is why all blood only believers still have their sins intact. But the believers who believe in the whole full gospel of the water and the Spirit have no more sin, and only there obedient people are called the children of God. God cannot call a sinner His child.