The relationship between OD&D and AD&D

 AD&D is what OD&D was starting to be. When E. Gary Gygax sat down to solidify his open notes of OD&D into the more concrete rule books of AD&D, he spent a lot of time explaining what he actually meant by the rules and pinning them with mechanics. Unfortunately in the process, he included a lot of extra elements that complicated or contradicted the rest of the structure. To really understand the game of OD&D, you must add to it cues from AD&D, or take AD&D and subtract elements from it until you return to a game that's like OD&D.

Most players, on the other hand, want to play the game their way, and rather use OD&D as a springboard for their own Fantastic Medieval Wargames Campaign, with the elements they like and rules assumptions that they prefer. And that was the original intent of OD&D all along.