The Nasuverse (emphasis on Tsukihime) muddles the meaning of "vampire" quite a bit. There are two categories — "True Ancestors" and "Dead Apostles" — detailed below, but all vampires generally lack the classical weaknesses. The only ones that seem to be true are that they have trouble with large bodies of water and are weak to sunlight, though this applies more to Dead Apostles. True Ancestors merely don't like it. Holy powers do work on them, but they're not particularly effective.
True Ancestors are the original vampires, spirit beings so powerful they can manifest in a physical form. They were willed into being by the planet itself as a self-protection program against the spread of humanity. They don't need to drink blood at all, but because the Crimson Moon tricked Gaia into using him as the template, they have a desire for it so powerful that they must use their own power to suppress it. If their will fails, they go insane and become Demon Lords, so the sane True Ancestors created Arcueid to deal with them. Apart from Arcueid and Altrouge (who is a hybrid of True Ancestor and Dead Apostle), they are considered to be extinct.
Dead Apostles, the other category, are a bit more complicated. A Dead Apostle is created either when another vampire sucks their blood or when their research into immortality reaches the point where they enter this category. For the first category, they begin as zombies, become mindless ghouls and another step or two with long periods in between until finally they are a vampire. The odds of any one zombie becoming a vampire is very low, but magical potential boosts both the odds and the rate as seen with Satsuki Yumizuka, who became a Dead Apostle literally overnight. Unlike the more powerful True Ancestors, Dead Apostles (particularly their leaders, the Dead Apostle Ancestors) tend to have some extremely bizarre form or ability, with such wonderful specimens as a bird-man, a vampiric mobile forest, a man who has turned himself into a mass of chaos, and a magus who literally transformed himself into a phenomenon. Some beings are classified as Dead Apostle only because they act somewhat like them, however, such as ORT or Primate Murder.
In Fortune Arterial, where many vampires strive to fit in among normal humans, their need for blood is similar to a substance addiction that has to be periodically quenched, and they also possess none of the traditional weaknesses, but cannot make more vampires via feeding. Rather, one who consumes a vampire's blood becomes a kenzoku (progeny,) gaining the abilities of a vampire (minus blood-sucking) but becoming bound to that vampire as a servant and an all-day breakfast on legs. While blood bags are commonly used, they cannot sustain a vampire forever—eventually, they will have to suck the blood of a human. Vampires typically make a contract with a human who becomes their servant and provides them with a source of blood, in exchange for immortality. The vampires also have the ability to erase memories. Also, while their eyes are not normally red, they do turn red when sucking blood or using their memory-erasure.