No, it says "not like" referring to the nature of the covenant. And yet it uses the exact words "my torah" (my law) which is exactly what was in the first version of the covenant. And once people's nature's have changed and the Torah is inscribed in our hearts, our previous state of sinning will not be remembered for punishment.
The talmud explains the answer to your question about who ultimately forgives -- the answer is God forgives but only after one has apologized/made restitution/sought forgiveness from a person he wronged.
Where does the concept of Ben Adam Lemakom and Ben Adam Lechavero come from? I know there is a concept of the first five of the ten commandments being between 'man and his friend' and the second ...
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