Vampires are blood-sucking creatures from mythology and folklore from all over the place, though I don’t (yet) know where the first vampires showed up…the modern iteration started sometime in the…17th century? I’ll have to check.
I personally think that Vampire: the Masquerade has the best vampire lore in terms of a cohesive story.
Buuut…I think that, maybe, Vampire: the Requiem actually does a better lore-job overall, though there are parts of Masquerade that are better. Requiem is at least better for mixing and matching.
Oh, right, half-vampires half-humans are called dhampirs.

I fist heard of Underworld in reference to a lawsuit filed by White Wolf against it. This is because White Wolf felt their copyright was being infringed in regards to the World of Darkness. It was settled out of court, though.
Underworld and Masquerade have very surface-level similarities, but are quite different. First, vampires aren’t dead…vampires are living creatures and, specifically, an immortal sub-race of humanity.
They’re immortal, drink blood and can turn others via a bite…and, well, the sun hurts them. They’re also directly related to werewolves and exist in a vampire faction, similar to the Camarilla…I guess.
Though there is only one faction in this world…though, keep in mind that I only watched the first two films.
The origin story for the vampires is that there was a guy named Alexander Corvinus who got infected with the Plague but, instead of killing him, it made him immortal. He had three sons. One of them was bitten by a wolf, which is where all the werewo- I mean…Lycans came from. One was bitten by a bat and that one was responsible for all vampires. Then the last one was just a normal guy.
However, there’s a worldbuilding issue here. Vampires cannot be descended from bats because vampire bats don’t live in Europe. This is actually an interesting quirk of vampire lore…since, well, as far as I can tell…the connection between vampires and bats is retroactive. Though all that matters is the fact it’s a mistake.

This also includes the Chronicles of Darkness.
I consider the World of Darkness (Vampire: the Masquerade) to have the most definitive portrayal of the vampire. Not only does it account for multiple kinds of vampires, but it also has detailed lore on the history of vampires…as well as a lot of really good worldbuilding, like the Masquerade, which just makes logical sense.
However, after thinking about it for a while…I came to the conclusion that Masquerade doesn’t really have the definitive vampire…with Requiem having that instead. The reason for this is that Requiem’s clans are more broad archetypes, while the Masquerade clans are very specific and detailed. Of the Masquerade clans, I think only the Ventrue can be ripped out of Masquerade and plopped into another setting without it being obvious that they came from Masquerade.
For an example of the other side of the coin: the Toreador. They’re generally viewed as the ‘sexy’ ones…but they’re also obsessive artists who can freeze in place to appreciate a sunrise. The Nosferatu are another example. Sure, they’re ugly and whatnot…but they’re also very good at gathering information, are extremely tight-nit and build sewer fortresses.
Masquerade’s bigger contributions (which can be pilfered for other story ideas) are the Masquerade itself and the vague structure of the Camarilla. Though for more broad vampire tropes, Requiem is likely better suited.

Vampires have an interest in using unequal (temporal) hours. Why?
Because temporal hours are defined as 12 day hours and 12 night hours. Normally, the times when night ends vary by day because the positions of the Sun and Moon vary day-to-day and depending on the Season. On the other hand, temporal hours are always based around when the day/night ends. This makes them extremely useful for vampires. Though the only real issue is that the length of an hour varies, at least you can keep track of exactly when the sun comes up.