Types of Possessions in Dragon Age world
Monsterification:
The possession can involve strong emotions but doesn't have to (it depends on the case, as it's hard to assume rocks or dead bodies have emotions, but places within the game can have lingering echoes of strong emotions that make such possessions more likely to occur within such area - spirits will just possess whatever).
It's unclear if such possession needs consent to occur.
The possession can be forced by a third party.
The person that gets possessed gets horrifically transformed.
The transformation can't be reveresed after it happens.
The person is driven mad by the transformation.
The possession can be prevented by Litany of Andralla.
Example: Slavren (DAO), Witherfang (DAO), Olivia (DA2)
There are other types of this type of possession that include objects, animals, plants or even corpses. It includes creatures such as: Sylwans (possession of a tree), Arcane Horror (possession of a mage's corpse), Rock Wraith (possession of a rock), Reverant, Skeleton (possession of a corpse), werewolf (possession of a wolf) and more similar cases.
Puppet:*
Person that gets possessed is trapped in the Fade.
Demon takes over the body and wrecks havoc all around, but isn't physically present inside the body of the host (?).
There is no transformation of the body.
The person can be saved by killing the demon in the Fade.
Needs established consent (with demon it will be a deal).
Examples: Uldred (DAO), Connor (DAO)
Teacher:
Person that gets possessed is a living willing host.
It's the opposite of the Puppet - person and the spirit coexist in a type of symbiosis, while the person is taught by the spirit.
There is no visible transformation of the body.
Person and a spirit can be separated via special rituals.
Example: Sigrid Gulsdotten (DAI: Jaws of Hakkon)
Impersonator:
The possessed person is already dead.
Spirit / demon is convinced they're the dead person or posses all the memories of the dead person as if they were them. (Demon may refer to the host as "food" separating itself from the host, while spirit will be confused by the memories of the body).
There is no visible transformation of the body, in fact the body is to some extent preserved thanks to the possession. (In case of a demon there is a second voice hearable when the person speaks).
Example: Sophia Dryden (DAO: Soldier's Peak), Kristoff? (DAO:A)
Revival:
The possessed person is already dead.
The spirit enters the body of the dead person and revives them. It's unclear if the spirit simply ties the soul of the dead person back to their body or assumes the role of said person. (It's quite possible that the spirit could think they're the person that already died or that the soul of the dead person turned into the spirit).
No visible transformation of the body, voice or personality.
No emotional outbursts.
Example: Wynne (DAO), Evangeline de Brassard (novel: Asunder)
* Could be also a different type of Merging described below.
**If we consider what happened to Evangeline the spirit may simply just attach itself to the soul and provide a link to the body (so called "spark of life") that is maintained until the spirit leaves the body.
Merging:
The possessed person is a living willing host.
The spirit and the person merge into one being.
It's not possible to separate them as they're already one.
No visible transformation of the body. (Possible visible veins of the Fade light and change of the voice when the spirit is fronting).
Possible emotional outbursts. (Due to taint corruption?)
Possibly person and the spirit loose sense of selves with time to become a fully integrated single personality.
Needs established consent (with demon it will be a deal).
Example: Anders (DA2), Flemeth (DAO, DA2, DAI)
Note: I wanted to add Cole here, but when I was writing down the criteria I noticed for possession I realized that Cole is a spirit that impersonates the dead person, not a spirit that took over his body. (Correct me if I'm wrong here, because I'm pretty sure he was seen as a free roaming spirit that just looked like a human - like the spirits of the old that could just randomly take on the mortal looking body).
*I just realized I forgot about one case of possession. Amalia from Stone Prisoner DLC. It's similar case to Puppet, but the difference is that the demon is already physically in the mortal world (?). It inhabits a body of a cat and tries to convince Amalia to willingly give her body out. When Amalia gets possessed she gets possessed in the mortal world by a demon that was trapped in the mortal world - her body doesn't change. When Amalia attacks you she doesn't turn into an Abomination monster model, she turns into Desire Demon itself.
^ TBH I'm still not sure if Demon is in the mortal world or in the Fade. As the difference between location is barely discernible in the game. So it's hard to say if demons we meet are in the Fade or mortal world.
Veilguard spoilers below:

















