Still it cannot be rightly inferred from this that believers have no need of the law. It ceases not to teach, exhort, and urge them to good, although it is not recognized by their consciences before the judgment-seat of God.
Is he speaking of two different laws? Yes and no. What he means by 'law' in the case of conscience is the law or covenant of works, i.e. the law as a means of justification. If one is to seek justification, i.e. assurance of conscience, via his works as measured by the law then he is done for. Game over! Even if he were to keep the entirety of the law and yet fail at only one point - one thoughtless inclination or impure thought - then he would be guilty of the entire law (James 2:10) and put under its condemnation. And even more, if one were to attain to living completely righteous before the law there would still be the matter of his former sins. Sins which, according to the same law, have earned him a death sentence. There simply is no peace nor help to be found in the law for the troubled conscience.
Yet for the one in Christ, who has been justified solely on the basis of faith, Jesus' perfect obedience and his payment for sin satisfies the law of works. For the believer the law takes on a new dimension. Yet it is still binding. That is what Calvin is referring to in the above quote. The law no longer judges but guides and directs the believer in the way of obedience. For in his place Christ has already been judged under the law. Are we commanded to obey? Yes. Are we still called to perfect obedience? Yes. But we are no longer judged by our works as measured by that law - rather by grace through faith in Christ.
The believer's relationship to the law has been forever transformed by the death and resurrection of Jesus. And so as those who believe in Him we no longer need to obey the law... What?! Are you saying that it is OK if we sin? Well, you sin, don't you? Of course you do. All believers sin. So in other words, when we sin (failure to obey the law in any way) we are no longer judged according to the law's demands but according to grace. This is an amazing thing. The righteousness we have is the righteousness of faith, not that of the law through our works. This first liberty we have as Christians is that for Christ's sake we have been set free from the law as a covenant of works so as to no longer be under obligation to meet its demands for righteousness. We are now set free under a new covenant, the covenant of grace. Calvin:
In regard to this liberty there is a remarkable passage in the Epistle to the Romans, where Paul argues, "Sin shall not have dominion over you; for ye are not under the law, but under grace," (Romans 6:14.) For after he had exhorted believers, "Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof: Neither yield ye your members as instruments of unrighteousness unto sin; but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God;" they might have objected that they still bore about with them a body full of lust, that sin still dwelt in them. He therefore comforts them by adding, that they are freed from the law; as if he had said, Although you feel that sin is not yet extinguished, and that righteousness does not plainly live in you, you have no cause for fear and dejection, as if God were always offended because of the remains of sin, since by grace you are freed from the law, and your works are not tried by its standard.