The believe something exists is to have an opinion that something is real and exists. To believe something happens is to have an opinion that something happens.
To know that something exists or happens is to have a belief that something exists or happens, when that belief is factually correct. The correctness of an opinion is what makes the difference between it being a belief and being knowledge.
People can say that they know something in the sens of being totally convinced it is correct,while being totally wrong about it and actually not knowning it.
I note that it is logical for the ideology of the watchers and the slayers to claim that a person's soul goes on to the afterlife when they die and become a vampire and that nothing remains of the human in a vampire body when they slay it.
Obviously such a belief would enable the slayers to slay vampires without feeling as much guilt as they would feel if they thought they were killing the human as well as the deomon.
I note that when Faith killed a human man, Buffy acted like Faith had crossed a Moral Event Horizon.
Even though Buffy and Faith had both killed many intelligent beings and persons before.
So Buffy seemed to have the ideology that only one species of intelligent beings, Homo sapiens, mattered or had the right to live, and it was okay to kill countless thousands of members of other species, such as demons.
If that was the ideology of the watchers and the slayers, naturally they would want to believe that they weren't killing a human inside the vampire body when they killed a vampire demon.
There was one episode where Willow met an alternate universe vampire Willow and later said that her vampire self seemed to be gay, and said that no doubt the vampire personality was totally different from the human personality.
And Angel said something like: "Not in my experien___" before shutting up. And Willow later did have a lesbian relationship.
And what about Angel's soul, if souls exist in the Buffyverse. Angel was a man who was shired and became a vampire. And one time he killed a beloved gypsy princess, and a Gypsy witch or wizard put a curse upon Angel, giving him a soul, and making Angle feel guilty for all the crimes he committed.
So if a Gypsy sorceress can create such apowerful spell, why didn't some Gypsy sorceress use a powerful spell to stop the Nazis when they slaughtered hundeeds of thousand sof Gypsies or Romani during WWII?
Later, Angel had sex with Buffy, triggering the senseless clause in the curse that he would lose his soul if he experienced enough happiness. Angel became the evil, souless Angelus again, inflicting horror and suffering upon many innocent persons, until that part of the curse was reversed by another human spell.
So when Angel's body died, his soul should have gone to Heaven or Hell according to the Christian religion and stayed there forever. So when the curse gave Angel a soul, was his original soul ripped from heaven or hell and returned to his body, even though he then experienced a lifestyle which was better than Hell but not as good as Heaven, and so was a different condiiton from what he deserved according to he judgement of God Almighty?
Or did the Gypsy curse on Angel make or find a second soul to give to Angel. And when the utterly senseless clause in the curse took Angel's original or second soul way, what happened to that Soul?
And then some of the scooby gang performed a magical spell that gave Angel a soul - it is unknown whether it was his original soul, or his second soul, or a third soul somehow created or acquired from somewhere.
So apparently mere mortal humans can perform spells powerful enough to change the fates of human souls. Apparently overpowering the rules of God Almighty, who is suppsed to omnipotent and powerful acording to Christian theology. And even a human magic user as sweet as Willow can turn evil - as Willow did a few seasons later - and should not be trusted with the awesome power to change the fate of human souls.
So some people might find the ability of mere human magic uses to change the fates of human souls in the buffyverse terrifying.
But do human souls even exist in real life or the Buffyverse?
Anyone who read Mary Shelley's Frankenstein (1818) knows that the creature turned evil because of his resentment at the way he was treated his creator, Victor Frankenstine. But in popular culture people often say the monster was evil because it had no soul. So those people seem to believe in all knowing and all powerful God who creates souls for every persons, but somehow made the obvious mistake of not giving the monster a soul.
Or maybe they are using "soul" as a metaphor for a conscience, a sense of right and wrong. I suspect that many people often use "soul" as a metaphor for a conscience.
And possibly the characters in the Buffyverse talk about human souls because they want to believe in human souls and life after death. Most of them should be familiar with Christianity, Jadaism, and Islam, and used to the concept of human souls and hope that souls are real. And seeing other "supernatural" things may make them more confident that souls exist. So they might believe that immortal souls already exist and there is need for them to find a way to create them.
But maybe the wish is the father to the belief, and maybe there is no evidence for the existence of souls in the Buffyverse.
I note that in "Welcome to the Hellmouth" Giles the Watcher said that the primordial Earth was a Hellish place instead of a Heavenly one in the beginning. So that makes it probabe that some parts of Christian theology - and possibly all of them - are incorrect.
And maybe the spells that kept giving Angel "souls" and taking them away actually gave and removed his conscience, and people simply used "soul" as a metaphor for "conscience" when talking about those spells.
Thus it is possible that in the Buffyverse there are no human souls and when a person's body dies, their personality, consciusness, and identity dies.
Except that when they are sired as a vampire, their persoanlity, identity, and consciousness remains in their body, along with that of the demon.
So maybe whenevr Buffy stakes a vampire, she is killing not only a demon, but whatever remains of the human the body belonged to.
In any case, it may be possible to say what characters in the Buffyverse believe about the fate someone who is vampirized. But it is impossible to say what those characters know about the fate of the vampirized, because someone can only know that which true, and it is impossible for viewers to know whether a Buffyverse character's beliefs are true in the Buffyverse.