Oh, on that fork lies madness. There's the Holmes (1978), B/X Moldvay (1981), BECCMI Mentzer (1983), Rules Cyclopedia and Black Box (1991) and Classic D&D (1994). The Holmes and Moldvay revisions each had multiple printings with different contents (so may have had different ISBNs, I couldn't find that info, though).
Oh, please don't get me started.
The other thing you have to remember is this-
OD&D (LBBs + Supplements) was the original D&D.
Holmes "Basic" was Dr. Holmes trying to rationalize and simplify
OD&D for newcomers. But, in the mind of Gygax and others, OD&D is what led to AD&D. AD&D is the successor to to OD&D (and Homes Basic). That's why it was originally called ADVANCED. You had Basic- what we would now call the "starter set" and then the Advanced Rules with all the bells and whistles. It's also why they added, before printing, the addition to Holmes Basic that if you wanted to play further, you should get the Advanced rules. Moreover, if you were following the hobby at the time, AD&D wasn't "new," it was mostly codified and edited OD&D rules at the time- those additional classes and materials were mostly drawn from supplements and Dragon magazine articles.
Moldvay Basic (B/X) was actually not based on Holmes, but it was also going back to OD&D, and while it went back to a lot of the early design decisions in the LBBs (minus the supplements) it also introduced some changes to streamline things- such as race as class.
So, while Moldvay Basic shares the name of Holmes Basic and some of the concepts (levels 1-3, for example, as well as looking back to the original OD&D rules) it's not exactly correct to say that Holmes Basic is the predecessor of Moldvay Basic; although it's not necessarily incorrect either.
There's an interesting article in Dragon 52 (Aug. 1981) where Holmes and Moldvay both discuss the new Basic. Holmes makes it clear that his remit and purpose was the clarify the OD&D rules, and states that, to the extent possible, he tried to use the original language of those rules. He also goes through the many changes of Moldvay Basic and his thoughts on them- but, to shed some light on the present conversation, he also repeatedly refers to Moldvay Basic as the "second edition."
Heck, the articles really speak to the whole mess all of this has been! The LBBs are referred to the Collectors Edition. Then you have the First Edition and Second Edition of the Basic Rules (thankfully, that never caught on). But the two editions are different, and have different purposes- the First Edition was created to be an introduction to the Collectors Edition for people who were not already playing, while the Second Edition was created because the market had changed and the "majority of D&D players are high-school and junior-high students."
