Ghost is the term used to refer to beings that, for some reason, cannot continue onto “some other world”.
In the world of summoning ceremonies, ghost are said to come from a place, not an individual. A ghost appearing usually means a gathering of power has been left wandering due to a few overlapping circumstances. Whether it is physical or a kind of data, it is common knowledge to summoners that the soul exists. And if some kind of conditions are thrown off, an error can occur and the soul of the dead will lose its destination. It will be stuck in the world like rainwater gathering in a drain clogged with leaves.
Ghost extermination is one of the most basic requests for summoners. Unless the ghost is a very powerful vengeful spirit, it is almost never necessary to fight the ghost with a Material. In most cases, one only needs to throw an Incense Grenade and set up an Artificial Sacred Ground. The ghost is a paranormal being, so the Artificial Sacred Ground will give them a boost and allow them to wield greater power than normal. However, they can not actually use that power. Once the conditions are set to summon a Material, the “clog” will be forcibly removed and the ghost will vanish like the rainwater left in the drain pipe. It is unknown whether it's simply a phenomenon being destroyed or if the soul really does go to heaven, but it does resolve the paranormal phenomenon. Very little is known about the phenomenon of ghosts, even by top tier summoners.