The answer is not clear cut at all. While there are enormous facts pointing to two different worlds, there are several facts pointing to one single world.
Facts supporting a unified world are the fact that during the last episode of the series:
After drinking the elders blood, she has a flash vision as her memories return. One of these memories during this time, and other times through out the series, is her fighting and killing a Chiropteran several times. Most of the flash visions are blurry, showing the shape of what appears to be a Chiropteran. In one of the last flash visions Saya has, it clearly shows her being attacked by a Chiropteran.
However, this could just be a coincidence if it was a joined but separate world, meaning that the two Saya's are different people. It is clearly stated that Saya is not the girls real name in Blood-C, that it was just a name given to her by her captor.
All in all, it is what ever you believe it is because the facts point to either side of the spectrum. you decide.