This article will address both changes in vampire myths that makes them more similar to elves/fairies/the fair folk/the gentle folk/the fey and the original similarities.
1. Uncanny Factor: This is an essential part of vampire mythology that horror fans do not complain about (as much). The basic idea that vampires, whether friendly or not, are not like us. They are not human, they do not think like humans, they are truly a different creature.
Elves, or the fair folk or the fey or whatever else you might call them, tend to share this trait. They have their rules, and will follow them strictly and expect you to, as well. What are they? I don't know them all. This was, again, an essential part of the scary part of the fairy lore. It was what made them scary, because you might do something that to us is, at worst, a minor faux pas, and then you look up and grin sheepishly and--poof. Or worse yet, just saying thank you.
2. Glamour: Ah, yes. Who can forget fey glamour? Besides, well, anyone the Fair Folk want to forget. That just goes without saying. Vampire glamour tends to work much the same way, with the creature in question having control over it, and strength varying, without varying too much in any one story--usually. Series, of course, explore this much more extensively.
3. Holy Objects: Yes, believe it or not, these originally worked on fey. This detail is usually glossed over or forgotten in modern myth, but it was present, nonetheless.
5. Hunting You Down: Think about this for a moment, for vampires. Does it really make sense? If the person tells anyone about vampires in a world where there is a masquerade of some sort going on, no one will believe him or her. If there is no masquerade (or this would break it, somehow), and the vampire wants to stop him or her anyway, then just kill the human. Vampires are superstrong, superfast, stuperstealthy, etc. Why not?
And the usual response is either nothing or that the vampire gets bored. If that's not it, then there might be rules governing treatment of humans to avoid detection, but then we get back to the fey very easily. There are strict rules for the Fair Folk to follow in most lore, and they had to be followed exactly. Sometimes, breaking them results in them being hunted down. This could mean being tossed out or getting the Wild Hunt after you.
(Incidentally, this is totally Sunday. And if it weren't, the fact that I had a bonus update this week would totally make up for it.)