Blood-Sucking Species

A general term for those that suck the blood of other living creatures.
Dead Apostles and True Ancestors both fall under this classification.
Although the terms vampire and bloodsucker were confusingly used to mean different things in Tsukihime itself, you can pretty much think of them as synonymous.
Creatures that suck blood are found all over the world, and they all have different characteristics. Because of that, the term bloodsucker is used as a catch-all term to describe them. In that sense, even Akiha would be considered a bloodsucker.
The Church concerns itself with the hunting of vampires specifically. That is, Dead Apostles and True Ancestors. Accordingly, they don't really care about things like the bloodsucking animals of South America, or the vampiric flying heads of mainland China.
Good news, eh, Akiha?

Tsukihime Data Collection: Tsukihime Dictionary
§

A general term used to describe organisms that consume the blood of their own kind.
Einnashe was a special exception as a subspecies of Blood-Suckers.
Most of the Blood-Suckers were weak against sunlight, but there were indeed Blood-suckers who were only active during the day.
The Dead Apostles of Tsukihime were representative of the Blood-Suckers. They were Blood-Suckers derived from mankind.

Yoi No Myoujou: Talk.
§

A general term for those that suck the blood of other living creatures.
Dead Apostles and True Ancestors both fall under this classification. Although the terms vampire and bloodsucker were confusingly used to mean different things in Tsukihime itself, you can pretty much think of them as synonymous.
Creatures that suck blood are found all over the world, and they all have different characteristics. Because of that, the term bloodsucker is used as a catch-all term to describe them. In that sense, even Akiha would be considered a bloodsucker.
Moreover, the Church concerns itself with the hunting of vampires specifically. That is, Dead Apostles and True Ancestors. Accordingly, they don't really care about things like the bloodsucking animals of South America, or the vampiric flying heads of mainland China.
Good news, eh, Akiha?

Tsukihime Dokuhon Plus Period: Tsukihime Dictionary Revised