I think the description of the world-of-darkness tag tries to hint at that but it's a bit vague. I'm a long time fan of the series, so to me "World of Darkness" tends to encompass all its incarnations, hence it needs a qualifier - "old" (oWoD) and "new" (nWoD).
I've been a bit out of the loop but I know of more recent developments - White Wolf started re-publishing some of the oWoD books and also putting out new ones. WW officially dubbed the line "classic" World of Darkness (cWoD) to avoid the moniker "old" as it was clear to existing fans but not to potential new ones. At a similar time, nWoD got its 2nd edition and was also rebranded as "Chronicles of Darkness" for...a lot of reasons. One of them being to differentiate it from the new books coming out as cWoD, as it could be confusing to see both at the same time, when they weren't actually about the same thing.
So, all in all, it turns out that there are the following terms:
- old World of Darkness (oWoD) - widely accepted fan made name to refer to the collection games published from the beginning of the 90s for about a decade. Officially only referred to as the World of Darkness. It spans multiple game lines and three editions worth of them. The editions are mostly compatible in a lot of respects, so they are rarely differentiated between.
- classic World of Darkness (cWoD) - a synonym for oWoD but comes from an official source - the developer White Wolf. It was introduced years after the game line ended, when WW also started publishing new materials for those game lines.
- new World of Darkness (nWoD) - widely accepted fan made name for a collection of games that started being published in 2004 by White Wolf and superseded oWoD which was over (at the time). Officially, the name is World of Darkness.
- new World of Darkness 2nd Edition (nWoD 2e) - an overhaul of both the mechanics, the cosmology, and focus of nWoD by Onyx Path Publishing, instead of White Wolf.
- Chronicles of Darkness - a sort of official nickname for the second edition. Best to just keep it simple like that. It also became the official name for the nWoD 2nd Edition forwards.
- At one point Onyx Path mentioned it could be "backported" to refer to the first edition of nWoD. I don't actually know if that was officially done (as in, complete re-branding), or was it just sort of accepted as convention but it's important to note that nWoD was not Chronicles of Darkness back when it began, it's a new term.
- World of Darkness - no qualifier. Could be used to refer to either of the oWoD or nWoD lines - official sources would just call that the current running series. It could also be used as a collective for both oWoD and nWoD, usually when talking about shared aspects. To add to that, there is a third official game called Monte Cook's World of Darkness. That can occasionally be lumped under the general WoD label but usually it isn't, since it's mostly different in mechanics, setting and scope.
- Then there are unofficial game lines like Genius: the Transgression (using the nWoD ruleset and universe) and Alternate World of Darkness (aWoD - using a very similar ruleset and universe to both oWoD and nWoD). Unofficial sources are also sometimes collected under WoD because they are similar enough in style, even if unofficial.
- Storyteller System - the official name for the oWoD ruleset. Could be used as a(nother) synonym for oWoD but it's rare, it usually means rule alone, while oWoD also includes in-game fluff.
- Storytelling System - the official name for the nWoD ruleset. Because naming both collections of game lines "World of Darkness" wasn't confusing enough, White Wolf had to make the ruleset names almost the same.
This is a bit of a background to show just how muddy the whole thing is with re-using names for different things, non-official (but widely accepted), and then official names and name changes, including backwards rebranding.
On this website, the relevant tags seem to be world-of-darkness, chronicles-of-darkness-1e, and chronicles-of-darkness-2e. So, while it does simplify the terminology a bit and makes sense when examined as a whole, it's not exactly clear when looking at the WoD tag individually. I posted an oWoD related question and I literally had to go through all three tags to even figure out which one to use because the WoD only hints at being oWoD related:
An urban-fantasy/horror game setting created by White Wolf Publishing, best known for its flagship game, Vampire: the Masquerade.
That's the entirely of the description. If you look at the terms above - "World of Darkness" has been known to refer to both oWoD and the collection of oWoD and nWoD - in both cases, Vampire: the Masquerade can be described as the flagship game. Perhaps to somebody with less background, it would be less confusing but, depending on what that background is (e.g., they've only seen nWoD) it could even be more confusing.
Looking at the synonyms helps to clarify things but if that's the requirement to find what the tag is, then that description fails at it purpose of describing the tag clearly.
I propose the tag be clarified more that it refers to the old/classic World of Darkness game lines. I'm not sure what the best wording would be but here is the description of chronicles-of-darkness-1e:
The Chronicles of Darkness (1e) games: a series of urban fantasy and horror games released by White Wolf starting in 2004 and later by Onyx Path. Games using the God-Machine Rules Update (aka the Second Edition rules) should use the chronicles-of-darkness-2e tag instead.
This seems very reasonable and clear. The description of world-of-darkness can be modeled to be like it - adding "for the games that started in 1991" and possibly mentioning "see chronicles-of-darkness-1e and chronicles-of-darkness-2e for newer game lines".