It's All D&D

Variations on a Theme
White Box is a creator's toolkit. The Little Brown Books are full of ideas, advice, rules and snippets which lead the reader to think about adding additional content. The Afterword at the end of Volume 3: The Underworld & Wilderness Adventures states:

There are unquestionably areas which have been glossed over. While we deeply regret the necessity, space requires that we put in the essentials only, and the trimming will often have to be added by the referee and his players.

The authors expect and encourage referees and players to add to the game. The entire game concept is one that demands creativity on the part of the players. Volume 1: Men & Magic tells us:

First, the referee must draw out a minimum of half a dozen maps of the levels of his “underworld,” people them with monsters of various horrid aspect, distribute treasures accordingly, and note the location of the latter two on keys, each corresponding to the appropriate level.

This creation task must be done prior to the first moment of actual play may begin.  Where does this "underworld" come from?  It must be imagined and drawn out from thoughts the referee has. There are helpful hints in Volume 3, but the "underworld" must be something original and unique, the creation of each referee. It is assumed by the authors that this underworld "building should be both easy and fun." In fact it is assumed that making the game your own is part of the fun.
The LBBs inspired a hobby and players have applied their creative talents to more than designing underworlds. Rulings become houserules and get printed and shared among others. Settings become so unique they they involve new player character classes, new races and new monsters. Eventually the game is barely recognizable and it takes on a different name. Today hundreds of roleplaying adventure games exist in publication (with different names due to copywrite laws), but they all hearken back to the original idea of a referee creating an imaginary setting for players to take the role of an individual character and have shared adventures. In a way, all of them are variations on a theme.
One of the two White Box authors, Gary Gygax, would write the three volumes of the Advanced Game with the intent of creating a "one true way" to play the game in reaction to the widespread modifications being made to the Original Game. I believe Mr. Gygax wanted to take creative control back and standardize play in order to make tournaments where everyone played by the same rules viable. Certainly the Advanced Game continued to be modified during actual play, but perhaps Mr. Gygax was at least partially successful because tournaments thrived, at least while TSR existed as a company and organized play is now quite popular, both depend on the acceptance of standardized rules of play.
The Original Game is an idea generator bound (and intended) to inspire modification. Returning to the comments in the Afterword which asks, "why have us do any more of your imagining for you?" The Afterword continues with the following advice: "the best way [to play the game] is to decide how you would like it to be, and then make it just that way!" I wonder if the authors imagined at the time that doing just that would result in such variety of play as is evidenced now by the multitude of available games. At times I think Mr. Gygax must have known people would "imagine the hell out of it" as one publisher says. After all, it is what he himself did with Dave Arneson's Blackmoor game (and what Mr. Arneson had done with the Braunstein game) isn't it?