So What are "History" and "Fiction," Anyway?

The terms "history" and "fiction" seem almost antonymous. The former refers to things that have happened, and the latter refers to things that have not; that someone made up. So how can these two ideas possibly combine to form such a thing as "historical fiction"? The way I see it, they can do so in one of three main ways:

1. Historical Setting, Fictional Plot:
Many historical fiction novels are just like any other works of fiction in that they tell of events that simply never happened. They do, however, place these fictional tales in a historical setting, making it so that they could plausibly have happened at some point in the past. The first book that pops into my head when I think of historical fiction is Rover, a book that I read several years ago. This novel tells the story of a Scandinavian girl (whose name I cannot remember) and her dog (whose name you can probably guess) through a Viking attack on their village that culminates in the girl being taken into slavery. The book then follows her subsequent life as a Viking slave. Now, it is certainly true that the Vikings attacked villages and took slaves, but the particular girl whose tale is told by Rover never existed. Her story, however, is typical of those of the thousands of girls taken as Viking slaves.

2. Historical Plot, Fictional Details:
Some works of historical fiction actually do tell of an actual event that happened in history. Take Ragtime, for instance. There was a person named Stanford White who was murdered by Harry K. Thaw of Pittsburgh during a performance of "I Could Love a Million Girls." The details of the murder and subsequent criminal case, however, do not match exactly those related by E.L. Doctorow in Ragtime. Ragtime, then, tells of a historical event with the help of fictional details, this blurring the line between history as fiction.

3. Historical Plot, Fictional Context:
This last one is a little hard to generalise. It is probably best exemplified by Libra, which tells the story of the assassination of President John F. Kennedy, a very well-known historical event, but which makes up an explanation as to why it happened that greatly differs from the official story. The main plot of the book is mostly non-fictional, but the set-up and behind-the-scenes action are definitely fictional.