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It's not so much about English definitions, as nWoD definitions.
So spirits are the spirits of a place, idea or thing. They represent that thing in the Spirit world and can have an impact on the thing they represent in the real world. So the Spirits of Christmases Past, Present and Future would work. They exist to further the needs of Christmas. In A Christmas Carol, that involved getting Scrooge to recognise the true meaning of Christmas so that he could celebrate it and encourage others to believe in the power of Christmas. A win for them.
Ghosts are just the souls of people who have died, trapped here by some unfinished purpose or business.
Geists are some weird hybrid of a ghost and a spirit of death. Over time, they come to symbolise the way they died. Marley was an unrepentant, avaricious, greedy sinner till the day he died a cold, soulless death. And so he works to cause more deaths like his, people who've lost touch with humanity just dying. But geists bond with people close to death sometimes, the better to carry out their needs and to feel a little human again. This makes a Sin-Eater. Clearly, Marley's Sin-Eater moderates that need to kill and first tries to find out whether the sinner really is irredeemable. Hence the plot.
Hell, maybe the narrator is a Sin-Eater. It would explain how he seems to get everywhere.