In Catholicism, what is the difference between Natural Law and Divine Law? In Catholic understanding, there is a divine law and a natural law.  Based on my reading, it seems like Divine Law = Revelation (as a Protestant would call it) and Natural Law = what you could deduce about right and wrong simply by using Reason to extrapolate the consequences of the act.

Thus, the 10 Commandments are first natural law (because you can figure out pretty easily that killing is bad), but then are also articulated by God. Does it then become Divine Law? Is it "also Divine Law" or "no longer Natural Law, just Divine?"

Are these categories supposed to exclusive? Is divine law higher than natural law?

Ultimately, what is the difference?
The overly simple answer is:  Natural Law is a human person's participation in the Eternal Law (the knowable part of which is called Divine Law).

While Peter Turner's answer covered all of the essential points, St. Thomas Aquinas' coverage of the topic is the benchmark among the Doctors of the Catholic Church and one summary of it (among many, I am sure) can be found here: Aquinas On Law.

The important parts:

Eternal Law is the mind of God as understood by God Himself.
Divine law is derived from Eternal Law as it appears historically to humans (revelation).

Natural Law, is tough to summarize succinctly. One decent summary is:


  The Natural Law, as applied to the case of human beings, requires
  greater precision because of the fact that we have reason and free
  will. It is the our nature humans to act freely (i.e. to be provident
  for ourselves and others) by being inclined toward our proper acts and
  end. That is, we human beings must exercise our natural reason to
  discover what is best for us in order to acheive the end to which
  their nature inclines. Furhtermore, we must exercise our freedom, by
  choosing what reason determines to naturally suited to us, i.e. what
  is best for our nature. The natural inclination of humans to acheive
  their proper end through reason and free will is the natural law.
  Formally defined, the Natural Law is humans' participation in the
  Eternal Law, through reason and will. Humans actively participate in
  the eternal law of God (the governance of the world) by using reason
  in conformity with the Natural Law to discern what is good and evil.


While not relevant to the original question, the final point is Human Law which builds on Natural Law. Saint Thomas says: 


  it is from the precepts of the natural law, as from general and
  indemonstrable principles, that the human reason needs to proceed to
  certain particular determinations of the laws. These particular
  determinations, devised by human reason, are called human laws. 
  (Summa Theologica q91, a3, p. 21)