As a hobby for nerds, there's a strong appetite among D&D fans to make lists and categorize things, and this extends not just to elements within the game but to meta-level discussion about the game itself. The most obvious breaking point is TSR-D&D (1974-97) and Wizards of the Coast/Hasbro D&D (1998-present), with the 1998-99 period (after Wizards took over but before D&D 3.0 was released) as a transition period. The next most obvious is the various editions: Original (1974-77*), 1st Edition Advanced (1978-88), 2nd Edition Advanced (1989-99), 3rd (2000-2007), 4th (2008-2013), and 5th (2014-present) editions. Neither of those really work for me, because my interests D&D-wise are sufficiently narrow that finer distinctions are warranted in order to pinpoint what I consider to be "the good stuff" vs the other junk.
One common taxonomy, as proposed by James Maliszewski at Grognardia (the influential, long-dormant but possibly newly revived "OSR" blog), divides the TSR/1st Edition era into a Golden Age (1974-83) and a Silver Age (1984-89), a distinction largely based on trade dress (but also perceived attitude changes that occurred in conjunction with the slicker and more professional upgrade in production values). The other common one differentiates between the Gary Gygax era (1974-85) and the post-Gygax or Lorraine Williams era (1986-97). I definitely buy into the latter, but even that is not a granular enough distinction for me, because it glosses over the difference between what Gary was doing himself and what the design department at TSR, the group originally led by Lawrence Schick and Tom Moldvay (who had been friends and collaborators before coming to work for TSR) that starting in 1980 reported to Brian Blume instead of to Gary, were doing at the same time. And that's not even to mention TSR-UK, which was a mostly-independent subdivision with their own writers, artists, and a subtly distinctive voice and style that's now commonly referred to as B-OSR and seems to have more kinship with what other UK game publishers were doing than what TSR in the US was.
And it gets even more complicated because Gary himself did a "soft reboot" on his approach to D&D c. 1975 when he handed the core of Greyhawk Castle over to Rob Kuntz and effectively started over with the Hommlet/Temple of Elemental Evil campaign. So even "Gygaxian" means different things at different times. I've seen a an explanation attributed to Gary that because Greyhawk Castle had been used for so much intensive play testing with a deliberately "anything goes" approach that it had become too sprawling and inconsistent and Gary wanted to separate that element (and the veteran players who were accustomed to that style) and keep the sub-campaign more grounded and structured and "pure" - developing what we eventually saw in AD&D, the modules, and the World of Greyhawk not just as an outgrowth from but in some sense also a repudiation of the earlier, more freewheeling and gonzo, Greyhawk Castle paradigm.
Take all of this together and by 1983-84 (the time that's most interesting to me because it's when I first discovered and got into the game) you've got a half dozen different takes on D&D with some degree of official support (not even counting all the other ways third party publishers and players out in the wild were drifting and modifying the game to their own ends):
1. Original Greyhawk Castle "we made up some shit we thought would be fun" style (also includes Blackmoor, Tunnels & Trolls, Arduin, Grimtooth's Traps, and most early Judges Guild)
2. Post-reboot "structured campaign" Gygax style (AD&D, World of Greyhawk, B1-2, D1-3, EX1-2, G1-3, L1-2, S1, S3-4, T1-4, WG4-6; IMO the Jennel Jaquays Judges Guild stuff (Dark Tower, Caverns of Thracia, etc.) also fits pretty solidly within this category)
3. Moldvay-Schick "customer-facing" style (less sandboxy and wargamery than #2; more focus on set-pieces and less on behind the scenes depth; more consumer-oriented as stuff to pull off the shelf and play through rather than stuff to add to your world - the B/X sets, Deities & Demigods, B3-4, X1-2, A1-4, C1-2, I1, O1, Q1, R1-4, S2)
4. TSR-UK "almost satirical" style (broadly similar to #3 but with its own distinct voice and aesthetic feel - White Dwarf magazine, Fiend Folio, U and UK series, O2, X8, Fighting Fantasy books, Citadel minis)
5. Tracy Hickman/Douglas Niles "I'm working on my novel" style (B5-7, X3-5, I2-6, N1, DL series, Ed Greenwood's articles in Dragon magazine)
6. Shovelware "going through the motions/paint-by-numbers crap" style (AC1-5, B8-9, X6-7 & 9, BSOLO, XSOLO, XL1, M1-2, CB1-2, MV1, N2)
#1 was pretty much forgotten by the time the 70s rolled into the 80s (and as an accident of fate is better represented and was preserved longer by third-party publishers, because TSR had already mostly repudiated this style by the time they ramped up production in the late 70s) so it felt like a genuine rediscovery when people found and embraced this stuff ~15 years ago, but I feel like that has since morphed into fetishization and groupthink, and refusal to acknowledge that this approach eventually grows stale.
#2 is my favorite and IMO the one worth preserving and emulating. It's what I've been talking about here for the last 3 years and in other places online for the 15 years prior.
#3 and 4 are what seems to be the most popular, both at the time and among the "grognards" at Dragonsfoot.org, in "1E" oriented Facebook groups, etc. This is probably because this style a little more accessible (and also a little bit easier - as in more carefully balanced and less deadly) than the #2 stuff. However, these fans either don't recognize (or do, but don't care) that it's also shallower and more limited than the #2 stuff - it's not as expandable, doesn't exist in a larger context, doesn't feel like something that might exist in the game-world whether or not the PCs are interacting with it, and so on.
#5 and 6 are, of course, what TSR fully embraced from 1986 until Wizards of the Coast took over and brought back a little bit of flavor from #2, a little more flavor and structure from #3 (i.e. a "story" built of strung-together but individually free-standing set-piece encounters), and a whole lot of deckbuilding and "rules mastery" mind-poison.
"Era-based" taxonomies (like Grognardia's) never really distinguish between #2-4 because they were all roughly synchronous with each other in the so-called "Electrum Age" of transition between the Golden and Silver Ages. Most fans even within this "old-school" niche-within-a-niche seem to engage only with the surface and are blind to anything but trade dress, cover artist, and logo. Module S4 obviously (at least to me) has much more stylistically and game-design-wise in common with G1, EX2, and WG6 (fellow "category 2" products with different trade dress) than it does with A4, B3, or X2 even though the latter all have the same yellow corner-flag trade dress, "face" logo, and Erol Otus covers. But if you try to bring this up to most fans, you're almost invariably going to get back something along the lines of "all I know is we had a great time playing through A4 - [insert favorite set-piece: the myconids/the cave fisher/the final battle on the docks] was awesome!"
Like everybody else who started playing D&D in the 80s I owned and played stuff from all of these groups (except #1, which I only discovered later) side-by-side and although I instinctively turned up my nose at the group 5 and 6 stuff even then, it was only long after the fact, looking back on all of it from a different perspective, that I also perceived the difference between #2 and #3/4, and realized that my interest and sympathies were really only with the former, and that that position puts me outside of the "mainstream" of even old-school/retro/OSR/grognard/whatever D&D fandom pretty much everyplace except The Knights & Knaves Alehouse, the seemingly one-and-only active online refuge of the hardcore Group #2 Gygaxians. But hey, at least I've got my tribe, small as it may be.
*of course some version of original or "classic" D&D remained in print through 1996, the D&D Basic Sets of 1977, 1981, and 1983 were, by all accounts, TSR's all-time best-selling products, and the 1991 D&D Rules Cyclopedia is Wizards of the Coast's current pdf/print-on-demand bestseller at DriveThruRPG, so defining the "Original D&D era" as ending in 1977 is unfair and not technically accurate. Nevertheless, from the time of its release AD&D always received the lion's share of attention both from TSR and the public and the non-Advanced version was mostly an afterthought, something mostly targeted at kids and beginners who were expected to "graduate up" to AD&D in fairly short order. There's a reason why 5th Edition is numbered that way - it's effectively the 5th version of AD&D. The widespread embrace of the "classic" version of the game and the way it's come to eclipse the popularity of AD&D even among "old-schoolers" is entirely a phenomenon of the 21st century - people who played AD&D (1E or 2E) as kids looking back and realizing that they now prefer the version they dismissed as "kid stuff" the first time around.