Probably the two biggest covenants in the Old Testament are the Abrahamic covenant and the Mosaic Covenant. The Abrahamic covenant promises three things: to make Abram's name great with a promise of many descendants, to give him and his descendants land, and to bless the world through Abram. The Mosaic covenant was quite different but with similar flavor. This covenant was a renewal of the Abrahamic covenant, but with conditions. The Law was given to the Israelites in hopes of making them into the people that would eventually be the blessing that was promised in the Abrahamic covenant. In Exodus 19: 4-6, God says if you obey my commands. This if was to say that when you obey my commands, you will be a blessing to all people and a blessing to Him. However, if they did not obey the commands, they would not reflect the nature and holiness of God, and therefore not be a blessing to others and to God.
My proposal here is that the covenant with Moses and the people of Israel was not needed until the time of the Exodus. The Abrahamic covenant was a covenant made with Abraham and his family. We are talking less than 100 people. As time goes on, Isaac, Jacob, and Joseph reproduce and begin to fulfill the promise of making Abraham a great nation. By the time of Moses, Israel is huge. It is said that there were over 600,000 men who came out of Egypt when the Israelites were finally delivered. This is significantly larger than 100 people. The point I'm attempting to make here is that one man (Abraham) can lead a small group, especially a family, in the way of the Lord. But when the family grows to at least 600,000 men with probably over 2,000,000 people when you add the women and children, it becomes difficult to keep up with and scold each one of them individually. I believe that the Law was given so that everyone, who was not very close to Moses and Aaron, would know exactly what was expected of them by having this written Law. Also by having this written Law, most people would be familiar with it and help keep everyone else accountable for their actions when they were not "being a blessing."
In conclusion, is the Abrahamic covenant different than the Mosaic covenant? Yes, but the principles that are provided by the Law in the Mosaic covenant reflect what was already expected of Abraham and his family in the time of the Abrahamic covenant. The big difference comes when the condition if is applied in the Mosaic covenant.