I've always been a little confused on this point.
My (second-hand) understanding of Aristotle's difference between potential and actual infinity is this:
We all have an intuition of the counting numbers 1, 2, 3, 4, ... The idea that "there's always a next one" is encapsulated by the principle of induction, which says that "if n exists, so does n + 1".
That's potential infinity. There are infinitely many things, in the sense that there's no end to the list. We can go as high as we want. But there is no completed "set" of all those numbers.
On the other hand, the axiom of infinity says that there is a set, which is a thing that satisfies the axioms of set theory, that contains 1, and whenever it contains n it contains n + 1. [I don't care if you prefer to start counting with 0, makes no difference to this point].
So to me, potential infinity is induction; and actual infinity is the axiom of infinity. An ultrafinitist rejects induction; a finitist accepts induction but rejects the axiom of infinity; and an infinitarist (not a standard term) accepts both induction and the axiom of infinity.
Now I have also seen "actual infinity" meaning physical infinity: the idea that there might be infinitely many planets, stars, electrons, intervals of time, "causes," etc. One sees this usage in William Lane Craig's theology, pointing out that an "actual infinity," by which he means a physical infinity, must be absurd because it would be subject to the "paradox" (which is not really a paradox) that an infinite set can be placed in bijection to one of its proper subsets, as in Galileo's paradox or Hilbert's hotel.
I am wondering what Aristotle had in mind about actual infinity. Whether he meant physical infinity, or just a conceptually completed collection containing all the natural numbers.
And secondly, is there a standard set of definitions in philosophy to disambiguate these terms, such as "actual infinity" versus "physical infinity," where the former means abstract sets whose existence depends on the axiom of infinity, and the latter means an infinite amount of physical stuff.
Thanks for any clarity on this issue.