Apparitions

Spirits
Spirits cannot physically be touched and are mostly like fairies. They represent some kind of force or concept and aren't normally the souls of the deceased. Most spirits are faceless and barely have personality if they have any, yet there are two major exceptions to this rule.

Divine Spirits, which are explained on the Gods page.

Vengeful Spirits have much more sapience and are usually born from regrets or other strong negative emotions when a person dies or when a disaster occurs. They are among one of the most dangerous beings in Gensekai and Shrine Maidens are tasked with exterminating them if they cause trouble.

Ghosts
Ghosts are limited to humans, yet they are not required to be purely spiritual beings. Ghosts are born from the souls of humans with a strong emotional attachment to a high degree to a certain place or otherwise. They are not able to pass through objects and have physical bodies. It can be almost impossible to tell when you're interacting with a ghost as they look perfectly human and are even warm to the touch.

The best way to have a ghost move on is to show them they are dead; as they may be unaware of their situation. Providing closure or realization more usually makes them move on.

Phantoms
This is what is usually meant when someone speaks of a dead person, yokai, or human. Phantoms are the 'standard' ghostly being and are usually the souls of someone who has passed onto the Netherworld. They lose their conscious self and when looked at are similar to floating wisps. They can exist in both the spiritual and physical world (depending on the area. Graveyards for example have phantoms about). Under odd circumstances, Phantoms can be born from even inanimate objects.

Half-human Half-phantoms can be born there, and share two bodies. A human body which is colder then normal and a spirit body which manifests as an ethereal orb that floats around the human body, which is warmer then normal. These people exist in a state between life and death.