In Vampire: The Masquerade, why do some abilities cost Blood Points while others cost Willpower? Is the distinction arbitrary, or is there a reason?
Vampires in V:TM use blood to fuel most of their supernatural abilities. Blood points are spent to heal, wake up from a day's sleep, power some disciplines, and to increase physical attributes, amongst other things. It means spending the blood to activate the inherent power contained within the blood. Spent blood means you later on need to refill and spending is limited to how much blood your vampire has in his body and by generation -- most neonates and PC vampires will only ever get to spend 1 blood point per round.
Blood pool is generally filled up very quickly and easily -- an average human vessel contains 10 blood pool, more than enough to fill up almost any PC vampire of average generation (12 or 13) after a single feeding.
Willpower is a measure of a vampire's inner drive and competence; in other words, it is a measure of a vampire's ability to achieve it's goals. It can be spent to do things such as avoid succumbing to the Beast or Rötschreck, to temporarily overcome a flaw or weakness, to temporarily suppress a derangement from manifesting, and to gain automatic successes. It is probably the single most used character resource in VTM. A vampire's current (not max) willpower score is also used as the difficulty for Dominate levels 1-4, among other things. Willpower is representative of a vampire's own emotional, physical, and spiritual (if such can be said about a vampire...) state and is not necessarily powered by anything supernatural.
Spent willpower is a measure of how mentally fatigued a vampire has become after resisting or overcoming such effects, and is restored through confidence in his or her own abilities. Willpower generally restores at a much lower rate (depending on your Storyteller), because it is awarded when a vampire PC acts true to her Nature, achieves a goal, or when a Story (not a session) is completed. Upon waking, each vampire also regains one willpower point. Awarding of willpower points is largely at the discretion of the Storyteller but it's also not unheard of to ask or nudge your ST if you think you've acted in accordance with your Nature, completed a goal, or overcome some obstacle and you think a willpower point may be due.