Is there any difference between an axiom and a postulate?
I would say that while an axiom is any proposition fixed as true without premises in a theory, a postulate is (also according with its etymology postulatum = something that is requested) something that is necessary to assume to make a theory fit (also in a consequential way) with some kind of experimental measurement. Is there any convention about it?
Axiom is rather well-defined. It's a unprovable cornerstone statement of a logical system. You cannot disprove it – if you can show an axiom is wrong with the tools from the logical system it founds, you didn't disprove the axiom, but the logical system (or made a mistake).
A postulate is something you mentally work with as a "given" to form a tractable hypothesis or derive a falsifiable result, prior to being able to prove it.
So, a postulate can turn out wrong (in which case it's simply a fallacy) or right (in which case it becomes a theorem).
In a practical context, we often do not inspect the truth of a postulate any further – it's a didactic tool that we often use as shortcut as in
The apple falls from the tree in a straight downwards line; you can prove that with Newtonian mechanics based on gravity, but this is 8th grade of school so maybe stick with us while we learn how a ball flies when thrown horizontally.
"The apple falls from the tree in a straight downwards line" is definitely not an axiom. No system I'm aware of needs fruit dynamics as fundamental statement to be somewhat complete. We postulate it does, because as soon as we look closer, things just become intractably complicated within the context we're working in.
