As the site's top expert on the Hunger Games, I should probably weigh in on this.
Individual-book tags are more useful in HG than in many other franchises.
In Lord of the Rings, for example, the three books form a unified narrative, and I think  Tolkien didn't even intend the story to be a trilogy. In Harry Potter, the seven books are separated by year and can be viewed as stories of their own, but there's a large extended universe around them and most of the HP questions don't relate to any particular book in the series.
In The Hunger Games, the three books are telling very different stories, and most questions are only relevant to one of them. The first book is the only one which covers a conventional Hunger Games, and it's not about much other than that. The second book covers the highly unconventional Quarter Quell, as well as the beginnings of a secret uprising. The third book is totally different, set mostly in District 13, all about open war rather than Games and subterfuge. Each book has a mostly different set of characters (rather necessary when most of the characters who appear in each book get killed off). Thus, it makes sense to tag, for example, questions about the war with mockingjay, questions about the Quarter Quell with catching-fire, and questions about Cato or normal Hunger Games procedures with just the-hunger-games.
The tag for the first book is the same as the franchise tag ...
This could be a potential issue, I'll admit. However, we're fortunate in that many of the general questions about the franchise are most relevant to the first book! Things like How are multiple volunteers handled during the Reaping? or Why are there so few volunteers in the Hunger Games? or Why couldn't tributes keep the food from the Launch Room?, which are about the Hunger Games as a whole, aren't so relevant to the second book (everything is different in the Quarter Quell) and not at all to the third book. So ambiguity between questions about the whole franchise and questions about the first book isn't that big of an issue. Also, since it's the first book, it can't spoil anything else. People reading book 1 might want to put the book 2 and 3 tags on ignore, but not vice versa.
What about book vs film tags?
Again, we're fortunate in that the films (which are, I'll come out and say it, an excellent adaptation) stuck reasonably close to the books. The first book and film are telling the same story with the same title; so are the second book and film; and the third and fourth films are both titled Mockingjay something, so they can fit under the mockingjay tag together with the third book.
TL;DR: as well as denoting different works of sci-fi, which tend to get their own tags, these tags also broadly categorise different types of question within the HG franchise.