It's it important, legal concept of imminence. It's self-defense if somebody points a gun at you, and you kill them in response. It's murder if you go to somebody's house, find them, and kill them because they hang out with bad dudes.
The al-Awlaki case was more like the latter example. He was accused of being a propagandist for al-Qaeda. He had not taken up arms, he had not engaged in violence, and any threat he posed was not imminent.
Moreover, the Obama administration recognized this, and argued that the President's assessment constituted due process of law, without the courts. Practically speaking, it means that the President can charge, try, and carry out the sentence of death, and there's no responsibility on anyone's part to prove that it was justified.
The upshot is that, for example, the President can now say that you're an "antifa terrorist," and execute you, even if all you did was post a meme mocking Hegseth, and you have no recourse.