Dark souls does not use a magic bar and instead uses a specific limited number of casts per spell, equipping two of the same spell will double the casts etc.
Demons souls has a hub and you teleport to the areas you will explore from it and have to sit through a loading screen to get to each one of them, whereas Dark souls is all connected except for one or two areas.
Demons and Dark souls both have different weapon upgrade systems, I personally like Dark souls system better.
Slightly different enemies.
Dark souls is a bit more polished, being made after Demons souls was.
The atmosphere in Demons souls is arguably a bit stronger than in Dark souls.
In Demons souls you heal with grass and collectibles and in Dark souls you heal with an estus flask that refills at bonfire checkpoints.
World Tendency is in Demons souls only.
Demons souls has a plunging attack and probably several mechanical differences that I am missing here.
But in all probability you didn't care about any of that.