4 KudoZ points awarded for this answer. Comment: "Thank you very much to both answerers. I researched both terms, and found this article: "An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually exclusive nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems. In Zermelo-Fraenkel set theory (in the form omitting the axiom of choice), the Zorn's lemma, trichotomy law, and the well ordering principle are equivalent to the axiom of choice (Mendelson 1997, p. 275). In contexts sensitive to the axiom of choice, the notation "ZF" is often used to denote Zermelo-Fraenkel without the axiom of choice, while "ZFC" is used if the axiom of choice is included." So apparently these are two different concepts (although it says they are equivalent)."