“Is the remission of sins the same thing as the forgiveness of sins?”
Bible words can often be defined by the way New Testament writers quote the Old Testament. For instance, we know that the words deliverance and salvation are the same, for when Paul quotes Joel, he changes the word “deliverance” to “saved” (Joel 2:32; Rom. 10:13). In the same way, we know that remission and forgiveness are the same, for in quoting Jeremiah, the writer of Hebrews changes the word “forgive” to “remission” (Jer. 31:34; Heb. 10:17,18).
In addition, we know that God set Christ forth “to be a propitiation… to declare His righteousness for the remission of sins that are past” (Rom. 3:25). That’s not talking about the sins that are past in your life, that’s talking about the remission of the sins of Old Testament saints like Abraham and David. So when we read that Abraham was also “justified” (Rom. 4:1-3), and David was “forgiven” (Rom. 4:7), we have to conclude that the remission of sins is tantamount to justification as well as forgiveness.
Finally, if you look up the word “remit” in a good dictionary, one of the words used to define it is “forgive,” and vice versa. source

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