What is the difference between a law and a theory?
A law describes what is the case, and a theory tries to explain something.
When we claim that all matter is made of atoms, we have these restrictions:
- We cannot look directly at an atom and say "here's one atom!" (unless we have some very special equipment, which was not available in the time of Aristotle and Democritus). They are too small.
- Matter is not atoms; matter is claimed to be made of atoms. That is the proposed explanation, or theory.
So, it cannot be observation, because at the time the theory was proposed, we couldn't observe atoms directly. It cannot be law, because a law states what is the case, and doesn't explain how it may or may not occur.
A separate example is the law of gravity.
We say that an object denser than air (a condition) will fall towards the Earth, no matter what. It's not a matter of how the object will fall; it's a matter of the fact that it will fall when it satisfies the condition.
A "theory" about gravity could be that it is an invisible force that pushes down on everything denser than air. It's not necessarily true, but it is still a theory.