Then the Lord said to Moses, “Write down these words, for in accordance with these words I have made a covenant with you and with Israel.” So he was there with the Lord forty days and forty nights; he did not eat bread or drink water. And he wrote on the tablets the words of the covenant, the Ten Commandments (Exodus 34:27-28).
Do you find something curious here? God commanded Moses to write down "these words." What were "these words?" In the immediate context, they were all the commands that God had just spoken to him beginning with Exodus 34:11. God says that "these words" are the basis of His covenant with Moses and Israel. And this understanding is supported by the introductory words of God in Exodus 34:10.
"These words" are not the Ten Commandments (lit. "ten words"), as we know them from Exodus 20. Yet, we are told in the very next verse, in Exodus 34:28, "He wrote on the tablets the words of the covenant, the Ten Commandments." Deuteronomy 10:2-4 tells us that God wrote (i.e. "by the finger of God") the Ten Commandments Himself. Therefore, the "He" in Exodus 34:28 most likely refers to God rather than Moses.
So what did Moses write and what did God write, and which relate to the covenant that God made with Moses and Israel?
It appears that God wrote the Ten Commandments (i.e. "the ten words") Himself on the stone tablets (Deuteronomy 5:5-22). These would be put into the ark of the covenant as a memorial.
It appears Moses wrote down "the commands, decrees, and laws" (cf. Deuteronomy 5:30), perhaps on a parchment scroll. I'm thinking that these words were too many to put on two tablets that he carried. Later, God commands the Israelites, after they entered the Promised Land, they were to set up two large stones, coat them with plaster, and write down "all the words of this law." These were not stone tablets to carry but large stone slabs to set up.
Now, what about the covenant. Was the covenant only with respect to what God Himself wrote, or also what God told Moses to write down? From our text, the covenant is associated with both what God wrote (Exodus 34:28) and what Moses was commanded to write (Exodus 34:27). Therefore, God's covenant with Moses and Israel was based on all the words of the law.
Why is this significant? There are some that try to argue that Christians are still under the Ten Commandments, though free from the "civil" and "ceremonial" commandments of the Mosaic Law. Yet, with respect to the covenant, such distinctions do not exist. And we learn from the Book of Hebrews that the old covenant, not in part but the whole, has been replaced by the new covenant in Christ:
But in fact the ministry Jesus has received is as superior to theirs as the covenant of which he is mediator is superior to the old one, since the new covenant is established on better promises. For if there had been nothing wrong with that first covenant, no place would have been sought for another... By calling this covenant “new,” he has made the first one obsolete; and what is obsolete and outdated will soon disappear (Hebrews 8:6,7,13).
With Christ's death on the cross, the old covenant was replaced by the new covenant, the Law of Moses by the Law of Christ (cf. Ephesians 2:15; Colossians 2:14; Romans 7:6; 2 Corinthians 3:6-11; 1 Corinthians 9:20-21).
There are two applications here:
First, because Christians are no longer under the Old Covenant (i.e. The Ten Commandments + commands, decrees and laws, approx. 615 in all), we should not feel compelled to obey any of the commands connected to the Old Covenant in the Old Testament. This includes the command to keep the Sabbath, the command to tithe, and the command to eat only kosher foods. What is more, we should not claim any OT promises based on the Old Covenant, as many prosperity preachers do. In the same vein, we should not be concerned that we will incur any of the curses associated with the Old Covenant. This would include the popular notion of "generational curses". We are set free from all these things in Christ.
Second, Christians are under the New Covenant, where God has promised that His principles would be written on people's hearts (cf. Hebrews 8:7ff; Jeremiah 31:31ff). These principles are largely explained in the New Testament epistles. Now, there are some significant overlaps with the commands in the Old Covenant, but this does not mean that the Old Covenant was, thereby, reinstated but rather that the significant moral and spiritual characteristics of the Old Covenant endured into the New Covenant. Therefore, even though it is true that Christians are no longer under the Mosaic Law, this does not mean that they are lawless. For we are under the Law of Christ, the new way of the Spirit, the law that gives freedom.