[redczar]

Axioms and postulates as Euclid uses that term are the same thing. In modern times we have gotten rid of the idea of statements that are self evidently true. So we don’t use the term postulate. We’d call Euclid’s postulates axioms today.

[eru]

Though to be honest, by modern standards Euclid sneakily uses some extra assumptions in his proofs that you actually need to add as axioms.

See https://math.stackexchange.com/q/1901133/1051561 for some examples.