I've not thought that the term Ballad referred to structure, but it had to tell a story. I found a while ago that almost all the ballads I sing are about death, but then I realized, what other story is going to have a song made about it.
In my experience, ballads that sing about current events are called contemporary ballads, and ballads that sing about actual past events are sometimes called historical ballads. So I infer that the default ballad is set in the past, and is often fictional.
I grew up with an album of murder ballads and one of ghost ballads, by Paul Clayton and someone else shelved alphabetically nearby (but I don't recall which was which anyway), and lots of folk songs. I tended to enjoy singing the ballads because they were long and told a story, and only realized later how very, very few of them were not a story involving death... ?