What does an axiom mean?
Statement or proposition which is regarded as established, accepted or self-evidently true.
Axiom is a statement or could be a proposition which we have arrived at by observations (or some other logical conclusions) and which we use as a basis to establish a model. I am calling it the ‘basis’ because we don’t fall into the cycle of questioning the axioms again and again. We may not have a concrete proof for an axiom strictly speaking but the axioms appear to be so self-evident by observation or inductive arguments that we “assume” it to be true. Like the assumptions of the model of electrostatics are the basic axioms on which we have structured the entire electromagnetism. It seems pretty right because every new idea fits into this and it gives us predictions that we experiment on and till now they have turned out to be very precise.
Now, as for option (A) a law can be an axiom but not necessarily so. For B, calling a definition (something we come up with) as an axiom is like saying “My name is the ‘king of the world’” and I am going to tell you how to rule. So yeah! Something like that.