The reason the two things connect, of course, is that salvation and redemption deal with sin. It is the answer to sin. If you don't have the question right, you won't have the answer right either. For example, Christian Science denies the reality of human sin. Therefore, within Christian Science, or other cults, or religions that deny the reality of human sin, there is no concept of salvation or forgiveness.
Original sin has to do with our state, that is, our condition.
That derives from the sinful acts of our first parents.- from Adam. From the moment that a person comes into existence, from the time of his conception, he is, as a matter of fact, a sinner. His status is that of a sinner. Now, that is true even before he commits any sinful acts himself. If one doesn't see this, one will treat very young children as if they are perfectly all right.