In what sense are we under the Ten Commandments and the rest of the Law of Moses?


We are not under any of the law including the Ten Commandments in any sense. Rom.6:14 is very clear that grace not law is the realm we now live. Some interpret the Bible to make a distinction between the moral and ceremonial law. They then suggest that while we are not under the ceremonial law, we are still bound by the moral law. The problem with this theory is that the Bible never makes a distinction between moral law and ceremonial law. Every statute binds those who are under the law; they cannot choose certain parts of the law to obey. James 2:10 makes this very clear. We who live during the dispensation of grace, however, are granted a position in Jesus Christ without having to keep any aspect of the law (Rom.3:28). There is a tremendous difference between law and grace. Notice the difference between law and grace with respect to the Sabbath day (the fourth of the Ten Commands. Exodus 31:14 under the law states that anyone who fails to keep the Sabbath shall be put to death. Col.2:16 under grace states that no one can judge  you on your choice to observe or not to observe the Sabbath.