Not that I mean when a servant takes over the body of a person, like Ruler jeanne, muramasa shirou, ishtar Rin or Parvati sakura, incarnation I think is called.
Pseudo-Servant, actually.
Servant -
The normal ones.
EMIYA, Medusa, Arash, Gilgamesh, Blackbeard, Elizabeth Bathory, Miyamoto Musashi, etc.
Shadow Servant -
'False echoes' of Servants, not fully summoned, and generally cannot use any NPs.
Tons and tons of these, potentially formed from any Servant.
Pseudo-Servant -
Servants summoned into the body of a living individual, with the closer the 'ideal' between them, the better the end results. HS generally takes control of the body to a large degree.
Waver, Ishtar, Ereshkigal, etc.
High Servant -
A Servant that is actually made up of several individual Heroic Spirits in a conglomerate 'composite' mass mind.
Moriarty, Sitonai, Scathach-Skadi, Lakshimibai, Meltryllis, etc. Sitonai is technically this and a Pseudo-Servant.
Grand Servant -
Seven Servants
* meant to fight the Beasts of Humanity.
Potentially can OHKO any/all other Servants, but have to cast away their 'Grand' status (temporarily until unsummoned) to do so.
King Hassan, Super Orion, Romulus-Quirinius, Solomon (ex-Grand Caster), etc.
Demi-Servant -
Similar to a Pseudo-Servant, except that the HS does NOT override the body's mind, and instead the body/soul/mind of the host body is fully in control.
Mash is the sole
confirmed one in FGO, although Grey
potentially is an Assassin Pseudo-Servant, as she might be hosting the spirit of Artoria[Assassin], who also has Carnwennan.
Card Servant -
Cards that allow an individual to briefly possess the powers, skills/abilities, and even Noble Phantasm, of whatever Heroic Spirit is 'printed' on the Card. EXTREMELY unique circumstances.
Currently only known to exist within the Prisma timeline. Anyone possessing one can briefly become something similiar to a Demi-Servant, but with minimal mental bleed over.
* Potentially there is a Grand for every Class, but Nasu isn't saying jack about any beyond the 'normal' seven.