My Calculus book from back in the day (Calculus Second Edition Michael Spivak) starts out by stating 12 basic properties of numbers which he labels P1-P12. He states:
"Most of this chapter has been an attempt to present convincing evidence that P1-P12 are indeed basic properties which we should assume in order to deduce other familiar properties of numbers."
I had always taken this to mean that those properties were axioms upon which (with the help of a few other properties) he was going to build up the whole of Calculus.
However, a google search for such a proof pops up the following link: https://proofwiki.org/wiki/Real_Addition_is_Commutative
Which purports to be be a proof of the Commutative Property of Addition of the Reals.
I then begin to question whether I even know what an Axiom is and look it up in Wikipedia arriving at: https://en.wikipedia.org/wiki/Axiom
Which immediately provides $a+b=b+a$ as an example of a non-logical axiom for which the terms axiom, postulate or assumption are interchangeable.