The point of distinction lies in the letter of the Law vs the Spirit of the Law. To live by God's Law is to understand and live by God's values and principles. Then there is the letter of the Law; the Mosaic Law. If you are under it then you must follow it to the letter; and it includes far more than simply moral laws. It includes a wide array of customs and traditions. Everything from what and how you eat to what you wear has guidelines.
It is true, by studying the Mosaic Law one may find God's Law. But blindly following the Mosaic Law as a list of do's and dont's does not equate to God's Law - it even displeases God.
Isaiah 1:10-15 Hear the word of the Lord, you rulers of Sodom; listen to the instruction of our God, you people of Gomorrah! 11 “The multitude of your sacrifices— what are they to me?” says the Lord. “I have more than enough of burnt offerings, of rams and the fat of fattened animals; I have no pleasure in the blood of bulls and lambs and goats. 12 When you come to appear before me, who has asked this of you, this trampling of my courts? 13 Stop bringing meaningless offerings! Your incense is detestable to me. New Moons, Sabbaths and convocations— I cannot bear your worthless assemblies. 14 Your New Moon feasts and your appointed festivals I hate with all my being. They have become a burden to me; I am weary of bearing them. 15 When you spread out your hands in prayer, I hide my eyes from you; even when you offer many prayers, I am not listening. Your hands are full of blood!