It's also TECHNICALLY not the same whip... It serves the same purpose, (and is named Vampire Killer after it get's the stake attatchment) but It's actual name is the Combat Cross.
Castlevania is no stranger to foreign Whips other than Vampire Killer.
Nathan Graves uses the "Hunter's Whip" if I recall. And Julius' apprentice in the Dawn of Sorrow novel sequel uses a "Holy Whip".
Let's all remember that this series isn't known for its consistency. It seems that in the classicvanias, you start out with a leather whip which changes form when up pick up the upgrade items. In the oldest games, there were only two forms (leather and chain). In CV4, there were three forms (leather, chain, longer chain). In Bloodlines, there were four forms (I forget what they were). etc.
In the starting with RoB, the VK doesn't receive upgrades and is a chain the whole time in 2D games. However, in the PS2 games, the VK seems to be made of leather (or some similar material).
Essentially, because of this inconsistency, it's impossible (or at least nearly impossible) to determine the true form of the whip.