I've written "scripts" that do things like create a user, run migrations, or do some processing on a file that pull in either or both of 3rd-party libraries or

I've written "scripts" that do things like create a user, run migrations, or do some processing on a file that pull in either or both of 3rd-party libraries or other code I wrote (ie. db models). So the "contained in a single file" for me isn't a hard requirement. I do think the rest of your points are accurate though. I'd also add that a script runs until the task is done, and no longer. Whereas you may have other programs, like web services or queue workers, that continue running and doing their tasks.