Between WoD and CoD: Not at all
WoD and CoD are not connected in any canon way. CoD is merely a spiritual successor of the WoD in many regards and at times shares names - which lead to some of the worst Edition Wars ever fought when CoD 1st Edition still claimed to be the (new) World of Darkness.
The Game Engines
Likewise, the Storytelling system is a spiritual successor of the Storyteller system. On a side note, the Storyteller system is a spiritual successor of Shadowrun, altering its d6 to d10 and removing the exploding dice from normal rolls.
Inside the WoD/CoD
Inside the WoD, all the splats inhabit the same world, and conflict between them is commonly referenced in all the splats books. The vast power-level differences though lead to huge fanboy-fights about which was the best Splat to wipe out all the others. Demons and Mummies always won for they came back.
As in cross-referencing, the three main lines (Vampire, Werewolf and Mage) regularly made referencing to one another and starting 2nd edition even contained stats for these splats when used as adversaries ported to the relative system.
Wraith's end was referenced heavily in Mage revised and became the start point for both Demon the Fallen as well as the last iteration of Mummy: the great Avatar Storm was what destroyed the Wraiths, released the Fallen and came right before the new life spell for the Amite.
Changeling is only passingly noted in Werewolf publications, usually when Arcadia is described.
The Metaplots of the WoD cumulate in plots like the Year of the Reckoning or Rear of the Scarab, where specific places are detailed from several sides, more elements are brought in and changes to the world introduced.
The end result of these Metaplots is the Year of Fire, which ends the WoD. At this point, the WoD really ends but how exactly is dependant on the players.
As the game aged, the 20th-Anniversary edition was made as a fix-up of the game system with a mix of 2nd and revised edition fluff. A lot of edition inconsistencies of the crunch were smoothed out. The general tone stayed, but at times it was modernized for a world that had aged and became considerably more technologically advanced.
The 5th edition is a rather recent upcoming. It is meant to bring a new system that still has the old roots, but so far only Vampire has made the release and I have not taken an in depth look at that. So I can just say "it exists and critics are divide about it". It is probably more of a Reboot.
The basic idea of all splats inhabiting the same world is also true for the CoD, but now the fanboy fights were dulled a lot as the system was much more streamlined. It was designed from the mortal up, not the supernatural down, and tried to even the playing field between Splats.
CoD 1e & 2e
CoD 1e and 2e are connected via the God Machine Chronicle plot, which somehow reminds of the Metaplots of the WoD, but is mostly meant to explain the changes to the background between the two editions.
Do you want to know more?
If you are interested in the history of one specific game, that'd be an excellent history-of-gaming question.