Paul made distinctions between the law (Mosaic) and grace because the Messiah had come. Every orthodox Jew, like Paul, knew/knows that when Christ came things would change, although they did not have a clue what that change would be. ie. would the law be abolished, how, then what
Here is a little trivia on what is considered "the law". Personally I believe they are guidelines, not law in the legal sense.
Historically, many of the laws that Israel used (10 commandments aside) paralleled, though they were modified, a version of the laws of the land that were in effect in Abraham's time. Those being the "code of Khummarabi" or Babylonian laws. In fact Abraham became royalty according to those laws, which is one of the reasons he could fight with the kings of the land there. Middle easterners still fight about those laws to date, mainly over land issues which those laws also pertained to.
Our English title for the book comes to us from the Greek and means "pertaining to the Levites." The priests of Israel came from the tribe of Levi and this book is like a manual for their call and function. The Hebrew title for the book comes from the first word of the book, meaning "And He Called" and emphasizes the theme of God's call to holiness
The title of the last book of the Pentateuch in the English comes from the Greek Deuteronomion, which means "the second law" or "the repeated law."
The book was given just before they entered Canaan in the 40th year after they had come out of Egypt ( 1:3 ). It was given because many of them had not witnessed the transactions at Mt. Sinai, the former generation having all died except Joshua and Caleb. It was given to impress their hearts with a deep sense of their obligation to God, and to prepare them for the inheritance which God had prepared for them.
While Leviticus was addressed to the spiritual leaders of Israel, Deuteronomy was addressed to the common people for every day guidelines for godliness.
The ordinances of Exodus, Leviticus and Numbers had regulated their nomadic life in the wilderness. Now as they were about to settle down in their own land some adjustments were necessary. This book provides these.
The only question a Christian needs to ask is, do I follow Moses or Jesus. Hopefully the Christian follows Christ.
Jesus did stand on a mountain and give His words to the people just as Moses had, but He gave them a new understanding with the beatitudes.