Holmes Basic is mostly an introductory set to OD&D, like the current D&D Starter Game Set is to 4E -- it only covers character levels 1-3, only covers dungeon adventuring (no wilderness, no castle-building or large-scale combat), and goes out of its way to actually explain how things work and why rather than just presenting the raw rules and leaving it up to the reader to figure out what it's all supposed to mean.
Why people consider it a separate edition from OD&D is because it was written and released during the transitional period when OD&D was being revised/expanded into AD&D and thus in several different places includes proto-AD&Disms that make it not quite compatible with OD&D -- there are spells on the Holmes spell lists and monsters on the Holmes monster list that weren't in OD&D but were in AD&D, the combat system in Holmes doesn't work quite the same way as the OD&D combat system (though for that matter it doesn't work quite the same as the AD&D combat system either -- what it's closest to actually appears to be "The Perrin Conventions"), and, perhaps most importantly, the Holmes set never refers the reader to OD&D for higher levels or more info, it always refers to AD&D (even though, at the time, AD&D hadn't actually been published yet, and when it was published wasn't nearly as compatible with the Holmes rules as OD&D was). So the Holmes set is really an odd orphan duck -- not quite OD&D, not quite AD&D, and not quite any of the versions of Classic D&D that came after.
As for the differences between B/X, BECMI, and the Rules Cyclopedia, it's mostly a matter of perspective. The Moldvay (1981) and Mentzer (1983) Basic Sets are ruleswise extremely similar (presentation-wise they're vastly different) -- the serious Moldvay- and Mentzer-ites at dragonsfoot can enumerate a handful of differences but they're all very minor (e.g. in Moldvay a magic-user or elf starts with 1 spell, it Mentzer he starts with 2 (read magic and 1 other)). The Marsh/Cook (1981) and Mentzer (1983) Expert Sets have more differences, because in the 1981 version character spells, saving throws, and abilities (thief skills, clerics vs. undead) essentially maxed out at 14th level, whereas the Mentzer version slowed down advancement to allow more room at the top -- so, from about 7th level on, Mentzer character abilities improve a bit slower than Marsh/Cook characters. Thus, while the Mentzer Companion (1984), Master (1985), and Immortals (1986) Sets could theoretically be used with the Moldvay and Marsh/Cook Basic & Expert Sets, you'd find some disparity as your 15th level Companion Set character has fewer spells, worse thief skills, worse saving throws, etc. than your 14th level Expert Set character did.
The Rules Cyclopedia (1991) reprints all the rules from the Mentzer Basic-Master Sets in a single volume, pretty much unchanged. The differences between it and the earlier version are that the advanced options introduced in the later Mentzer sets (such as the Druid and Mystic classes, the Weapon Mastery system, and the General Skills system) are included in the RC from level 1 (making for a more complicated game, and steeper learning-curve, right out of the gate instead of starting out simple and layering on complexity gradually), and that the Immortals rules were changed completely (in the product Wrath of the Immortals (1992)).
There aren't as many differences between any of these three versions as between AD&D 1E and 2E, or 3.0 and 3.5, but there are some differences (it's not like when TSR re-released the 2E books in 1995 with different art and layout but kept all the rules exactly the same) so, depending on how detailed you're getting in the conversation, or how much play you're actually doing, it is worth differentiating between them.
