Distinguish different notions of possibility, and explain how that bears on Aquinas's argument.

In the Summa Theologica, Thomas Aquinas lays out five ways (in Latin, quinque viae) to show God exists, also referred to as the proofs of God’s existence. Aquinas’s third way, which relates to contingency, is known as the argument from possibility and necessity.
Two contrasting earlier approaches to the possibility or necessity of existence are those of the Greek philosopher Aristotle and the sixth-century neo-Platonist John of Alexandria (or Johannes Philophonus). While Aristotle’s natural theology was based on an eternal cosmos with no beginning or end, it is considered anti-Creationist. John of Alexandria, critiquing Aristotle, argued against the eternity of the world or for an origin, or Creationism.
In his third way, Aquinas endorses the idea that something must account for the existence of the universe. The alternative would be that the universe, among the two possibilities, had not come into existence. Since it did, there must be a cause; it must exist by necessity.
Similarly, regarding all beings within the universe, Aquinas bases his argument departs from the idea of a possible being, one that is capable of existing and not existing. There are many natural beings, he argues, that are possible and subject to corruption or generation. As such a being is also capable of not existing, there must be a time at which it had not existed. By extension, if all beings were possible, then there would also be a time at which nothing had existed. If that were the case, nothing would exist now: no being can come into existence otherwise than through one already existing. In contrast, Aquinas offers a necessary being, one that is cannot not exist. Such a necessary being is not only necessary within itself, but can be caused to be necessary by another necessary being. This chain is not infinite, however, in regard to both efficient causes and necessary beings. For all beings that are dependent on something else for their existence, behind them must be something independent. That is a necessary being, or God.
https://www.britannica.com/biography/John-Philoponus

https://www.britannica.com/topic/the-Five-Ways