What’s the difference between the “Law of Moses” and “Law of God”?
The “Law of Moses” is a beautiful thing—when men regard it rightly. This is why the Psalmist can say, “O how I love Thy law” (Psalm 119:97). The “Law of Moses was not meant to save men, but to show them their need to be saved, and thus to lead them to Christ (Galatians 3:24). The Jews of Jesus’ day twisted the law, so much so that they considered themselves to be righteous, and yet they condemned Jesus as a law-breaker (especially in regard to the Sabbath—see John 5:16ff.; 19:7). This may help to explain why Jesus called the law “your law” in John 8:17, even as they called it their law (John 7:51; 19:7).
There is a great difference between accepting the Law of Moses as God’s standard of righteousness, and making that same law the means to earning your own salvation, by the work of law-keeping. In Romans chapter 3, Paul made it clear that no one could be saved by law-keeping. So it is that when Paul refers to the “law” in Romans 7, he is referring to the “Law of Moses” or to the commands of God more generally in the Old Testament. Paul loved the “Law of Moses” when it was looked upon as “the law of God” and not as that set of laws that were twisted by the Jews into something they were never meant to be.
In my opinion there is not a great difference between the “Law of Moses” and the “law of God” as mentioned in Romans 7. The difference is in how men looked upon that law. When they saw it is something one must keep in order to earn salvation (Jesus would call this “your law”), they were wrong. When they saw it as a standard of righteousness (Paul would call it, “the law of God”) which Jesus kept as the Son of God, and which the Holy Spirit strengthens us to keep (although imperfectly, see Romans 8:4) then they viewed it rightly.