I just got a hold of Dark Souls but I have never played Demon's Souls before. I know the games are related and was just wondering to what degree in terms of storyline, characters, etc.
According to the developers, Dark Souls is not a direct sequel of Demon's Souls but a spiritual successor. So the story are not related even though the mechanics are really close, and the game are made by the same director and producer.
"What we we want to clear up is this is actually not a sequel to Demon's Souls - we're treating this as a brand new game created by the same director and producer," Miyazaki-san told CVG in an interview.
"Again it is created by the same director and producer, so the base concept and themes are very similar. However, the story itself as well as a lot of the game features have been recreated so that we can present this as a brand new title."
It is stated in the beginning of Dark Souls, that in the age of ancients the world was filled with arch trees, and everlasting dragons and was shrouded by fog.
In Demon's Souls, when we first start off, the narrator explains how the fog swept across the land, killing much of humanity in the process. Demon's Souls contains arch trees and dragons.
So, yes, I believe it's in the same timeline, just pre-dating the Dark Souls games. (There are a couple other clues but I suggest you search for them yourself. Discovering lore in FromSoftware games is part of the fun)
Demon's Souls reveals that a divine creator named "Gawd" gave man a soul. He created the old one (the bringer of fog) to offset man. The great old one created demons to harvest the souls of man to grow his own power. Dark Souls makes no mention of the existence of Gawd or the old one, but we're left with demons, fog, the harvesting of souls for some unknown purpose, and of course several other characters, items, and locations, do carry over from Demon's Souls into Dark Souls. Instead of Gawd, or King Allant (who I theorize might be connected to the Old Iron King/Ichorous Earth of Dark Souls 2) we have Gwyn and his family, who are referred to as gods, but are really more akin to the Greek pantheon or some group of superior humans empowered by their own spells and equipment. Of course, we know about their conflict with the dragons of the grey, which should connect a few dots. I think FromSoftware is just doing their best to avoid legal trouble, as Atlus retained rights to the title "Demon's Souls," but Dark Souls might as well be titled "Demon's Souls 2." Personally, I love it. I think it adds to the mystery and depth of the story. I believe King's Field, Demon's Souls, Dark Souls, and Bloodborne, are all interwoven and tell a much bigger story than we're so far able to decode. It's beautiful.