My understanding on this question comes mainly out of a couple of scriptures in the Old Testament. These passages arise when the events of the Exodus are being reviewed and so are not close in the text to where the events happened.

They are useful, I think, because they do make direct statements about the laws involved, but one is towards the end of the Exodus text and the other is in Deuteronomy so they can be missed as they are not that close to where the events are detailed in Exodos 19 onwards.

We can get an idea of what is said about the laws that were put in the Old (Mosaic or Law) Covenant by first looking at Exodus Chapter 34 verse 28.

Exo 34:28 And he (Moses) was there with the LORD forty days and forty nights; he did neither eat bread, nor drink water. And he wrote upon the tables the words of the covenant, the ten commandments.

Here God has it recorded that what was written on the 'tables of stone' was The Covenant, and this was the Ten Commandments.

We can read the second reference I alluded to before if we now turn to Deuteronomy, chapter 4 verses 12-13. There we see this...

Deu 4:12-13 And the LORD spoke to you out of the midst of the fire: you heard the voice of the words, but saw no similitude; only you heard a voice. And he declared to you his covenant, which he commanded you to perform, even ten commandments; and he wrote them upon two tables of stone.

This second passage confirms the earlier one that the "Ten Commandments", which were written on two tables of stone, constituted the Covenant that God made with the Children of Israel. Of course there were other laws that they were given that as a nation they also were to keep, but the Old Covenant was according to these scriptures essentially based on the Ten Commandments.

This Law Covenant was unique also in that it was made with the Children of Israel and with no other previous group or individuals. It was only made with the nation of Israel as is pointed out in Deut 5:2-3...

Deu 5:2 Jehovah our God made a covenant with us in Horeb. Jehovah did not make this covenant with our fathers, but with us, even us, all of us here, alive today.

This seems to confirm what the Apostle John says in John 1:17...

Joh 1:17 The Law was given through Moses, grace and truth came through Jesus Christ.

So based on these texts the understanding is that the Ten Commandments were the basis of the Mosaic (Old) Covenant and that they were not part of any previous covenant that Jehovah made with the fathers of the nation, Abraham, Isaac and Jacob.

And, followers of Jesus now live 'not' by the law brought by Moses, but by the grace and truth that came through Jesus Christ.

Another thought....