Once upon a time, there was a company called White Wolf, who released a little game called Vampire. At the same time, they made plans for four more games in the same World of Darkness: Werewolf, Mage, Ghost, and Fairy – these were released in subsequent years, though Ghost had its name changed to Wraith and Fairy to Changeling. These were generally compatible, at least on the mundane level, though you'd need to file some sharp corners off to make various Kewl Powahs work.
Eventually, White Wolf ran out of Vampire books, and decided to make a 2nd edition, fixing up some mechanical issues and, having more cash because of the success of Vampire, prettifying the layout and stuff. This was also a pattern repeated with the other four RPGs. There were also some other branches, such as historical versions of the main games and others featuring other supernatural monsters (I know there was a Mummy and a Demon, but I can't recall if there were others).
All of the games had settings that expected Something Big to happen Some Time Soon. Vampires were expecting something they called Gehenna, Werewolves the Apocalypse, and so on. White Wolf were also pretty fond of metaplot, with various movers and shakers doing things that changed the setting in various ways in pursuit of these events, and with this metaplot being conveyed via novels and sourcebooks. Eventually they ran out of books again, and realized that the metaplot had made some things in the original books irrelevant (e.g. for some reason Malkavians had lost the Dominate discipline and instead gained the Dementate one), and so they released the Revised editions. I know Vampire, Werewolf, and Mage all got Revised editions, but I'm not sure about Wraith and Changeling – Wraith and Changeling were not as popular as the others.
Eventually, in the early 00s, the folks at White Wolf decided they couldn't really push the metaplot any more, and that the games had run their course, so they decided to go out with a bang. They released a series of three books: Gehenna for Vampire, Apocalypse for Werewolf, and Ascension for Mage, all describing the endgames of the respective lines. And then they were done.
Well, sort of. The old World of Darkness was replaced with a new World of Darkness in 2004, with a different system (you still had attributes and abilities rated in dots, and rolled d10s equal to the sum depending on what you were doing, but everything else was pretty different). Unlike the previous games, the new World of Darkness started out with a core book for playing regular humans (and I believe it also had rules for ghosts), presenting a mundane baseline. They then released new versions of Vampire, Werewolf, Mage, and Changeling (I don't remember if there was a Wraith version as well) but with different sub-titles. Vampire the Masquerade became Vampire: the Requiem, Werewolf: the Apocalypse became Werewolf: the Forsaken, and so on. These were basically whole new takes on the old concepts, and the new games at least attempted to focus on the personal level rather than the large-scale metaplot that to some degree had taken over the old versions.
These probably weren't as commercially successful as the old versions, and White Wolf eventually got sold to the Icelandic computer game company CCCP, mostly known for the MMO space game Eve Online. The intent was to make an MMO based on Vampire (and potentially other WW IP), but when CCCP had an economic downturn they axed that, and essentially White Wolf was no more.
Except... one of the old White Wolf people, Rich Thomas, started up a new company, Onyx Path Publishing, and licensed the rights to some of White Wolf's IP from CCCP. I'm not quite sure in which order they did things, but they kept publishing things for the new World of Darkness. As the 20th anniversary of the original release of Vampire approached (so around 2010), they also licensed the rights to do an anniversary edition of Vampire the Masquerade. This was based on Revised, but incorporated a lot of supplemental material (e.g. clans that weren't in the original rules because they weren't part of the Camarilla). It was primarily released via Kickstarter and DTRPG (as a POD), not via the traditional distribution chain, but became successful enough that they eventually did the same with the other four "prime" WOD games, and even got the rights to do a few supplements for the 20th anniversary editions.
Now, enter Paradox. Paradox has its roots in the Swedish company that used to make the games Drakar och Demoner and Mutant, as well as KULT, but are now a computer game company known for grand strategy games (like Europa Universalis, Crusader Kings, and Stellaris). But apparently the people running it wanted to get back into RPGs, and realized that White Wolf was owned by CCCP who weren't really doing anything with it other than licensing some things to OPP. So they approached CCCP, and bought White Wolf from them. They had a chat with OPP about licensing going forward, which resulted in the "new World of Darkness" being rebranded "Chronicles of Darkness", OPP buying some other properties from White Wolf/Paradox (notably Scion and Trinity), and continual licensing of others (like Exalted). Paradox then started making their new version of Vampire, which they called 5th edition (partially because they considered 20th anniversary its own edition, and partially because VV looks like a pair of vampire teeth). They included a bit more edgelordy stuff than recommended, particularly in supplemental material, which is what brings us to the situation referred to in the OP.
So TL;DR: There are two Vampire games: Vampire the Masquerade (originally released in ~1990) and Vampire the Requiem (originally released in 2004). VtM's version history goes 1st -> 2nd -> Revised -> 20th anniversary -> 5th edition, and VtR's goes 1st (as an expansion for World of Darkness) -> 2nd edition (as a standalone game incorporating the nWOD/CoD core rules). Most of the other WOD games have similar situations.
