"Adventure hook" is a common term.
While true, this is related to the second part of the previous post I quoted above. It feels like this entire disagreement over how your & story should be defined can be squarely attributed to a decade of 20104's PHB effectively guiding players to make whatever they want & expect it to work without consulting anyone while wotcstaff kept saying the ambiguous phrase "tell your story" without context or additional clarification making it clear if the phrase is directed to "you" personally the listener or the players who make up your group/table/party of fellow players & if that story is one that you control the telling of at an author type level or one where you merely participate in as one part of the whole