Are the Ten Commandments and the Natural Law one an the same? Are the Ten Commandments the codification of the Natural Law.
I wouldn’t say they are one and the same. The “Ten Commandments” entry in Modern Catholic Dictionary states:
With the exception of forbidding graven images and statues and the precept about the Sabbath, the Ten Commandments are an expression of the natural law.
Note it does not say they are equivalent. The Old Law, moreover, was incomplete; it found its completion only in the New. The Catechism teaches:
1965 The New Law or the Law of the Gospel is the perfection here on earth of the divine law, natural and revealed. …]
1968 …] The Lord’s Sermon on the Mount, far from abolishing or devaluing the moral prescriptions of the Old Law, releases their hidden potential and has new demands arise from them: it reveals their entire divine and human truth. It does not add new external precepts, but proceeds to reform the heart, the root of human acts, where man chooses between the pure and the impure,22 where faith, hope, and charity are formed and with them the other virtues. …]
Remember that (from a Jewish perspective) the ten commandments are really the ten categories as each commandment has its own subset of commandments. For example: Keep holy the Sabbath day has a lot of sub-commandments in order to know HOW to keep it holy…ie no lighting a flame on the Sabbath.
The short answer is “no”.
Natural Law is the law written in the hearts of men and the creation itself.
The Ten Commandments are particular positive law of the Creator Himself.
Except for the sabbath, the 10 Commandments do reflect the natural law–I would argue that even includes the command to love God above all things and to not worship created things as the Creator (this is the natural virtue of religion which falls under justice, not a theological virtue).
Because we are fallen and our appetites sometimes get the better of our reason, we can have trouble discerning these things from our natural reason alone. As such, God has also revealed them explicitly to us.
From the CCC:
1981 The Law of Moses contains many truths naturally accessible to reason. God has revealed them because men did not read them in their hearts.