I think largely this is correct. But if I may lay out what I understand it to be, for simpletons like myself:
From what I remember in grade school, when one has a
problem (for example, how did the universe come into being?, or how can we move something directly over a canyon?), one makes a testable
hypothesis as to the answer to the problem. One then tests the hypothesis with
experiments, and gets
results from the experiment. He may test many times before either abandoning the hypothesis as false, or reaching a
conclusion that the hypothesis does indeed seem to be true, or at least partially true. And scientists will
retest a theory many times to see if their tests reach the same conclusions. When a hypothesis is tested many times, in many different circumstances, to make sure no better hypothesis explains the results, the hypothesis is considered a
theory. If, after being considered a theory, nothing ever really challenges it, it can be considered a
law.
So...
Hypothesis, theory and law differ in kind, not degree.
Somewhat - in the same way a pond, a lake, and a sea are all bodies of water. A theory or a law just have more evidence for themselves than an hypothesis.
A hypothesis is a conjecture made to be proven or disproven, based on previous research. A theory is a field of study, particularly one involving a certain type of model. Therefore the phrase "Atomic Theory" means the models used to discuss the structure of the atom, not the question of whether or not atoms exist.
Actually, any student of atomic theory asks the question: "What is the structure of an atom?". The study is not of the "model", or theory, but of the question, and the apparent answer to it - that is, the theory. The difference being the theory is an
answer to a
question. It is not a session of hand-shaking and self-congratulating that we all agree on something.
A law is a simple physical relationship, usually expressed as a mathematical equation. There wasn't a time where, for instance, Newton's Laws of motion were known as Newton's theories of motion. They are laws because they can be stated succinctly and represented mathematically.
Einstein's theory of relativity - E=mc(2) - can be stated succinctly and mathematically. But it is not a law.
A law, simply, is a theory about which we are more or less certain given the overwhelming about of evidence in its favour.
Take for example the laws of the conservation of matter and energy. As the philosopher has said, "Ex nihilo nihil fit". From nothing comes nothing. It would be the end of science if anything could appear or disappear without any explanation whatsoever. Even Christians do not believe anything comes from
nowhere. That would be far too convenient.
But in our experience, everything comes from something else. Nothing disappears completely; it just changes into something else. If it didn't - if things popped into existence from nowhere, or disappeared into nothing, we have never observed such a thing.
It's interesting there has been no talk of axioms, since maths has been brought up.
It seems to me the natural sciences have no axioms.