But then for some reason, another company went back and restarted publishing the old lines
I think it was the same company. White Wolf published World of Darkness games using its Storyteller system from 1991 until 2004. They then made the move to Chronicles of Darkness (a retroactive title the only came about in 2015, until then they were also called World of Darkness officially, known to fans as “new World of Darkness”) in 2004. CoD changed some of the lore around and drastically cut back on how detailed and complex the metanarrative was.
CoD used their new “Storytelling” system, and did not perform very well commercially. Probably some fans didn’t like it much, but mainly they decided to stop selling in stores so there was no discoverability. During the CoD era, White Wolf still published some WoD material, such as the 20th anniversary editions.
The most important detail here though comes in 2015–2018. Up until this point White Wolf has been bought and sold a couple of times, most recently by CCP. In 2015 they are bought by Paradox Interactive. In 2018 they release VtM 5th edition. In response to allegations of some very problematic material in V5, Paradox dissolves White Wolf and brings WoD production into Paradox Interactive.
I think that only Vampire, Hunter, and Werewolf are currently supported in the latest edition of Storyteller, but I may have missed something.
It’s true that Onyx Path as a separate licensee has published books for White Wolf/CCP/Paradox. But they’ve done 20th Anniversary, CoD, and V5 stuff. The actual decision to go back to WoD was White Wolf/Paradox’s.