The ghosts are the transparent humans who have died and arrive in Grey Town. Most of the ghosts described by the narrator choose to get on the bus going to the Heaven-like location but do not choose to stay in Heaven. They return to Grey Town in their filmy, weak state to either stay there for eternity or to travel to "Heaven" again at some other point.
The Bright People and the Solid People are the same. Sometimes the narrator refers to them as Spirits. They are humans who died, went to Grey Town, traveled to "Heaven," and chose to stay there. From the narrator's description, the solid people have been in Heaven long enough to have traveled to the Mountains where they change from ghosts to bright/solid people. Their physical transformation symbolizes their getting rid of their sin or fleshly nature and becoming holy so they can navigate the grounds of Heaven easily. They're at home there, unlike the ghosts who have not yet chosen to relinquish their sin nature.
In each of the chapters featuring specific ghosts such as Big Man and Ikey, the narrator provides details about the ghosts' assigned "Spirits." The Spirits are not assigned randomly however. Shortly after the narrator descends from the bus, he says,
"I noticed that [the Solid People] were moving with order and determination as though each of them had marked his man in our shadowy company" (25).
The Solid People are able to recognize which ghost is assigned to them because they have some connection with the ghosts from their earthly lives. For example, one mother ghost who lost her son when he was a little boy encounters her deceased brother who is now a Solid Person; he is her assigned Spirit. His job is to explain how "Heaven" works and to try to encourage her to leave Grey Town permanently.
The narrator is himself a ghost, and his assigned Solid Person or Spirit is a real-life author, George MacDonald, who influenced C.S. Lewis's writing. Through much of the second half of the book, MacDonald mentors the narrator and explains why the choice between staying in Heaven versus returning to "Hell" is such a difficult one for the ghosts.